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Volumn 230, Issue 1, 2000, Pages 127-173

The Projective Geometry of the Gale Transform

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EID: 0034239481     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1006/jabr.1999.7940     Document Type: Article
Times cited : (66)

References (74)
  • 1
    • 0002506094 scopus 로고
    • Twelve associated points in [5]
    • Babbage D. W. Twelve associated points in [5]. J. London Math. Soc. 23:1948;58-64.
    • (1948) J. London Math. Soc. , vol.23 , pp. 58-64
    • Babbage, D.W.1
  • 2
    • 0002507811 scopus 로고
    • Ten associated points and quartic and quintic curves in [4]
    • Bath F. Ten associated points and quartic and quintic curves in [4]. J. London Math. Soc. 13:1938;198-201.
    • (1938) J. London Math. Soc. , vol.13 , pp. 198-201
    • Bath, F.1
  • 5
    • 0000776599 scopus 로고
    • Algebra structures for finite free resolutions, and some structure theorems for ideals of codimension 3
    • Buchsbaum D., Eisenbud D. Algebra structures for finite free resolutions, and some structure theorems for ideals of codimension 3. Amer. J. Math. 99:1977;447-485.
    • (1977) Amer. J. Math. , vol.99 , pp. 447-485
    • Buchsbaum, D.1    Eisenbud, D.2
  • 7
    • 51249166999 scopus 로고
    • Quadrics through a set of points and their syzygies
    • Cavaliere M. P., Rossi M. E., Valla G. Quadrics through a set of points and their syzygies. Math. Z. 218:1995;25-42.
    • (1995) Math. Z. , vol.218 , pp. 25-42
    • Cavaliere, M.P.1    Rossi, M.E.2    Valla, G.3
  • 9
    • 0000154622 scopus 로고
    • Point sets and allied Cremona groups, I
    • Coble A. B. Point sets and allied Cremona groups, I. Trans. Amer. Math. Soc. 16:1915;155-198.
    • (1915) Trans. Amer. Math. Soc. , vol.16 , pp. 155-198
    • Coble, A.B.1
  • 10
    • 84966202202 scopus 로고
    • Point sets and allied Cremona groups, II
    • Coble A. B. Point sets and allied Cremona groups, II. Trans. Amer. Math. Soc. 17:1916;345-385.
    • (1916) Trans. Amer. Math. Soc. , vol.17 , pp. 345-385
    • Coble, A.B.1
  • 11
    • 0000678296 scopus 로고
    • Point sets and allied Cremona groups, III
    • Coble A. B. Point sets and allied Cremona groups, III. Trans. Amer. Math. Soc. 18:1917;331-372.
    • (1917) Trans. Amer. Math. Soc. , vol.18 , pp. 331-372
    • Coble, A.B.1
  • 12
    • 18444388052 scopus 로고
    • Associated sets of points
    • Coble A. B. Associated sets of points. Trans. Amer. Math. Soc. 24:1922;1-20.
    • (1922) Trans. Amer. Math. Soc. , vol.24 , pp. 1-20
    • Coble, A.B.1
  • 14
    • 0002532696 scopus 로고
    • Basic systems of rational norm-curves
    • Conner J. R. Basic systems of rational norm-curves. Amer. J. Math. 32:1911;115-176.
    • (1911) Amer. J. Math. , vol.32 , pp. 115-176
    • Conner, J.R.1
  • 15
    • 0002594022 scopus 로고
    • The rational Sextic curve and the Caylay symmetroid
    • Conner J. R. The rational Sextic curve and the Caylay symmetroid Amer. J. Math. 37:1915;28-42.
    • (1915) Amer. J. Math. , vol.37 , pp. 28-42
    • Conner, J.R.1
  • 16
    • 0002410919 scopus 로고    scopus 로고
    • The Gale transform for sets of points on the Veronese surface in P5, "Pragmatic 1997, Catarcia"
    • Franco D. The Gale transform for sets of points on the Veronese surface in P5, "Pragmatic 1997, Catarcia" Matematiche. 53:1998;43-52.
    • (1998) Matematiche , vol.53 , pp. 43-52
    • Franco, D.1
  • 18
    • 0002490258 scopus 로고
    • Über das Raümliche Achteck welches die Schnittpunkte dreier Oberflächen zweiter Ordnung bilden
    • Dobriner H. Über das Raümliche Achteck welches die Schnittpunkte dreier Oberflächen zweiter Ordnung bilden. Acta Math. 12:1889;339-361.
    • (1889) Acta Math. , vol.12 , pp. 339-361
    • Dobriner, H.1
  • 20
    • 0003220018 scopus 로고
    • Points sets in projective spaces and theta functions
    • Dolgachev I., Ortland D. Points sets in projective spaces and theta functions. Astérisque. 165:1988.
    • (1988) Astérisque , vol.165
    • Dolgachev, I.1    Ortland, D.2
  • 22
    • 0037509462 scopus 로고
    • Syzygies of points in projective space and applications
    • Berlin: de Gruyter. p. 145-170
    • Ehbauer S. Syzygies of points in projective space and applications. Zero-Dimensional Schemes, Ravello, 1992. 1994;de Gruyter, Berlin. p. 145-170.
    • (1994) Zero-Dimensional Schemes, Ravello, 1992
    • Ehbauer, S.1
  • 23
    • 0000285638 scopus 로고
    • Linear sections of determinantal vertices
    • Eisenbud D. Linear sections of determinantal vertices. Amer. J. Math. 110:1988;541-575.
    • (1988) Amer. J. Math. , vol.110 , pp. 541-575
    • Eisenbud, D.1
  • 28
    • 0001959745 scopus 로고
    • Finite projective schemes in linearly general position
    • Eisenbud D., Harris J. Finite projective schemes in linearly general position. J. Algebraic Geom. 1:1992;15-30.
    • (1992) J. Algebraic Geom. , vol.1 , pp. 15-30
    • Eisenbud, D.1    Harris, J.2
  • 29
    • 0002525923 scopus 로고
    • An intersection bound for rank 1 loci, with applications to Castelnuovo and Clifford theory
    • Eisenbud D., Harris J. An intersection bound for rank 1 loci, with applications to Castelnuovo and Clifford theory. J. Algebraic Geom. 1:1992;31-59.
    • (1992) J. Algebraic Geom. , vol.1 , pp. 31-59
    • Eisenbud, D.1    Harris, J.2
  • 31
    • 0001157502 scopus 로고
    • Determinantal equations for curves of high degree
    • Eisenbud D., Koh J-H., Stillman M. Determinantal equations for curves of high degree. Amer. J. Math. 110:1988;513-539.
    • (1988) Amer. J. Math. , vol.110 , pp. 513-539
    • Eisenbud, D.1    Koh, J.-H.2    Stillman, M.3
  • 32
    • 0033474618 scopus 로고    scopus 로고
    • Gale duality and free resolutions of ideals of points
    • Eisenbud D., Popescu S. Gale duality and free resolutions of ideals of points. Invent. Math. 136:1999;419-449.
    • (1999) Invent. Math. , vol.136 , pp. 419-449
    • Eisenbud, D.1    Popescu, S.2
  • 33
    • 0002532698 scopus 로고    scopus 로고
    • Syzygy ideals for determinantal ideals and the syzygetic Castelnuovo lemma
    • D. Eisenbud. New York/Berlin: Springer
    • Eisenbud D., Popescu S. Syzygy ideals for determinantal ideals and the syzygetic Castelnuovo lemma. Eisenbud D. Commutative Algebra, Algebraic Geometry, and Computational Methods. 1999;247-258 Springer, New York/Berlin.
    • (1999) Commutative Algebra, Algebraic Geometry, and Computational Methods , pp. 247-258
    • Eisenbud, D.1    Popescu, S.2
  • 35
    • 0002670267 scopus 로고
    • Neighboring vertices on a convex polyhedron
    • H. W. Kuhn, & A. W. Tucker. Linear Inequalities and Related Systems. Princeton: Princeton Univ. Press
    • Gale D. Neighboring vertices on a convex polyhedron. Kuhn H. W., Tucker A. W. Linear Inequalities and Related Systems. Annals of Math. Studies. 38:1956;255-263 Princeton Univ. Press, Princeton.
    • (1956) Annals of Math. Studies , vol.38 , pp. 255-263
    • Gale, D.1
  • 36
    • 0001907912 scopus 로고
    • On Veronesean surfaces
    • Gimigliano A. On Veronesean surfaces. Indag. Math. A. 92:1989;71-85.
    • (1989) Indag. Math. A , vol.92 , pp. 71-85
    • Gimigliano, A.1
  • 37
    • 0001618196 scopus 로고
    • A new class of linear error-correcting codes
    • Goppa V. D. A new class of linear error-correcting codes. Problems of Inform. Transmission. 6:1970;207-212.
    • (1970) Problems of Inform. Transmission , vol.6 , pp. 207-212
    • Goppa, V.D.1
  • 38
    • 84955593036 scopus 로고
    • Codes and information
    • Goppa V. D. Codes and information. Russian Math. Surveys. 39:1984;87-141.
    • (1984) Russian Math. Surveys , vol.39 , pp. 87-141
    • Goppa, V.D.1
  • 40
    • 84972544398 scopus 로고
    • Koszul cohomology and the geometry of projective varieties, I
    • Green M. Koszul cohomology and the geometry of projective varieties, I. J. Differential Geom. 19:1984;125-171.
    • (1984) J. Differential Geom. , vol.19 , pp. 125-171
    • Green, M.1
  • 41
    • 0000505311 scopus 로고
    • Some results on the syzygies of finite sets and algebraic curves
    • Green M., Lazarsfeld R. Some results on the syzygies of finite sets and algebraic curves. Compositio Math. 67:1988;301-314.
    • (1988) Compositio Math. , vol.67 , pp. 301-314
    • Green, M.1    Lazarsfeld, R.2
  • 43
    • 0000897672 scopus 로고
    • Gorenstein ideals of deviation two
    • Herzog J., Miller M. Gorenstein ideals of deviation two. Comm. Algebra. 13:1985;1977-1990.
    • (1985) Comm. Algebra , vol.13 , pp. 1977-1990
    • Herzog, J.1    Miller, M.2
  • 45
    • 0001219275 scopus 로고
    • De curvis et superficiebus secundi ordinis
    • Hesse L. O. De curvis et superficiebus secundi ordinis. J. Reine Angew. Math. 20:1840;285-308.
    • (1840) J. Reine Angew. Math. , vol.20 , pp. 285-308
    • Hesse, L.O.1
  • 46
    • 0002415708 scopus 로고
    • Ueber die lineare Construction des achten Schnittpunktes dreier Oberflächen zewiter Ordnung, wenn sieben Schnittpunkte derselben gegeben sind
    • Hesse L. O. Ueber die lineare Construction des achten Schnittpunktes dreier Oberflächen zewiter Ordnung, wenn sieben Schnittpunkte derselben gegeben sind. J. Reine Angew. Math. 26:1840;147-154.
    • (1840) J. Reine Angew. Math. , vol.26 , pp. 147-154
    • Hesse, L.O.1
  • 47
    • 0002508379 scopus 로고
    • Bronx, New York: Chelsea Publishing
    • Hesse L. O. Gesammelte Werke. 1972;Chelsea Publishing, Bronx, New York.
    • (1972) Gesammelte Werke
    • Hesse, L.O.1
  • 48
    • 0002616023 scopus 로고
    • Multiplicity-2 structures on Castelnuovo surfaces
    • Hulek K., Okonek Ch., van de Ven A. Multiplicity-2 structures on Castelnuovo surfaces. Ann. Scuola Norm. Pisa (4). 13:1986;427-448.
    • (1986) Ann. Scuola Norm. Pisa , vol.13 , Issue.4 , pp. 427-448
    • Hulek, K.1    Okonek, Ch.2    Van De Ven, A.3
  • 49
    • 0001057095 scopus 로고
    • On Siegel modular forms of genus two, I and II
    • Igusa J. On Siegel modular forms of genus two, I and II. Amer. J. Math. 86:1964;219-246.
    • (1964) Amer. J. Math. , vol.86 , pp. 219-246
    • Igusa, J.1
  • 50
    • 0001875528 scopus 로고
    • Chow quotients of Grassmannians, I
    • Providence: Amer. Math. Soc. p. 29-110
    • Kapranov M. Chow quotients of Grassmannians, I. I. M. Gel'fand Seminar. Advances in Soviet Math. 16:1993;Amer. Math. Soc. Providence. p. 29-110.
    • (1993) I. M. Gel'fand Seminar Advances in Soviet Math. , vol.16
    • Kapranov, M.1
  • 51
    • 0042724739 scopus 로고
    • Some applications of the canonical module of a 0-dimensional scheme
    • Berlin: de Gruyter. p. 243-252
    • Kreuzer M. Some applications of the canonical module of a 0-dimensional scheme. Zero-Dimensional Schemes, Ravello, 1992. 1994;de Gruyter, Berlin. p. 243-252.
    • (1994) Zero-Dimensional Schemes, Ravello, 1992
    • Kreuzer, M.1
  • 52
    • 0002432358 scopus 로고
    • On 0-dimensional complete intersections
    • Kreuzer M. On 0-dimensional complete intersections. Math. Ann. 292:1992;43-58.
    • (1992) Math. Ann. , vol.292 , pp. 43-58
    • Kreuzer, M.1
  • 53
    • 0001516984 scopus 로고
    • Classification of the Tor-algebras of codimension four Gorenstein local rings
    • Kustin A. R., Miller M. Classification of the Tor-algebras of codimension four Gorenstein local rings. Math. Z. 190:1985;341-355.
    • (1985) Math. Z. , vol.190 , pp. 341-355
    • Kustin, A.R.1    Miller, M.2
  • 55
    • 0003321115 scopus 로고
    • Introduction to Coding Theory and Algebraic Geometry
    • Basel: Birkhäuser
    • van Lint J. H., van der Geer G. Introduction to Coding Theory and Algebraic Geometry. DMV Seminar. 12:1988;Birkhäuser, Basel.
    • (1988) DMV Seminar , vol.12
    • Van Lint, J.H.1    Van Der Geer, G.2
  • 57
    • 0002616646 scopus 로고
    • Curves and symmetric spaces, I
    • Mukai S. Curves and symmetric spaces, I. Amer. J. Math. 117:1995;1627-1644.
    • (1995) Amer. J. Math. , vol.117 , pp. 1627-1644
    • Mukai, S.1
  • 60
    • 84963483350 scopus 로고
    • Double structures on Bordiga surfaces
    • Rathmann J. Double structures on Bordiga surfaces. Comm. Algebra. 17:1989;2363-2391.
    • (1989) Comm. Algebra , vol.17 , pp. 2363-2391
    • Rathmann, J.1
  • 62
    • 0002532703 scopus 로고
    • Über linear abhängige Punktsysteme
    • Rosanes J. Über linear abhängige Punktsysteme. J. Reine Angew. Math. 88:1880;241-272.
    • (1880) J. Reine Angew. Math. , vol.88 , pp. 241-272
    • Rosanes, J.1
  • 63
    • 0002507813 scopus 로고
    • Zur Theorie der reciproken Verwandschaften
    • Rosanes J. Zur Theorie der reciproken Verwandschaften. J. Reine Angew. Math. 90:1881;303-321.
    • (1881) J. Reine Angew. Math. , vol.90 , pp. 303-321
    • Rosanes, J.1
  • 64
    • 0002533257 scopus 로고
    • The Noether-Enriques theorem on canonical curves
    • Shokurov V. The Noether-Enriques theorem on canonical curves. Mat. Sb. 15:1971;361-403.
    • (1971) Mat. Sb. , vol.15 , pp. 361-403
    • Shokurov, V.1
  • 66
    • 0000242802 scopus 로고
    • On the number of points determining a canonical curve
    • Stevens J. On the number of points determining a canonical curve. Nederl. Akad. Wetensch. Indag. Math. 51:1989;485-494.
    • (1989) Nederl. Akad. Wetensch. Indag. Math. , vol.51 , pp. 485-494
    • Stevens, J.1
  • 68
    • 0000704038 scopus 로고
    • Das Problem der Projektivität und seine Andwendungen auf die Flächen zweiten Grades
    • Sturm R. Das Problem der Projektivität und seine Andwendungen auf die Flächen zweiten Grades. Math. Ann. 1:1869;533-574.
    • (1869) Math. Ann. , vol.1 , pp. 533-574
    • Sturm, R.1
  • 69
    • 0002419739 scopus 로고
    • Über Collineation and Correlation
    • Sturm R. Über Collineation and Correlation. Math. Ann. 12:1877;254-368.
    • (1877) Math. Ann. , vol.12 , pp. 254-368
    • Sturm, R.1
  • 72
    • 85037794388 scopus 로고
    • Some combinatorial properties of complexes
    • Whitney H. Some combinatorial properties of complexes. Proc. Nat. Acad. Sci. U.S.A. 26:1940;143-148.
    • (1940) Proc. Nat. Acad. Sci. U.S.A. , vol.26 , pp. 143-148
    • Whitney, H.1
  • 73
    • 0002508381 scopus 로고
    • Some generalizations of Castelnuovo's lemma on zero-dimensional schemes
    • Yanagawa K. Some generalizations of Castelnuovo's lemma on zero-dimensional schemes. J. Algebra. 170:1994;429-431.
    • (1994) J. Algebra , vol.170 , pp. 429-431
    • Yanagawa, K.1
  • 74
    • 0002419025 scopus 로고
    • Note sur les huit points d'intersection de trois surfaces du second ordre
    • Zeuthen H. G. Note sur les huit points d'intersection de trois surfaces du second ordre. Acta Math. 12:1889;362-366.
    • (1889) Acta Math. , vol.12 , pp. 362-366
    • Zeuthen, H.G.1


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