Geometry and Algebra of Prime Fano 3-folds of Genus 12

Compositio Mathematica

Volumn 127, Issue 3, 2001, Pages 297-319

  Schreyer, Frank Olaf ^a  

^a UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

Fano 3 folds; Instable planes; Net of quadrics; Plane quartics; Polar hexagons; Sums of powers; Syzygies; Theta characteristics; Twisted cubics

Indexed keywords

EID: 0038564027     PISSN: 0010437X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1017529016445     Document Type: Article

References (29)

1. Arbarello, E., Cornalba, M., Griffiths, P. A. and Harris, J. (1985): Geometry of Algebraic Curves, Vol. I, Grundlehren Math. Wiss. 267, Springer-Verlag, New York.
2. Bayer, D. and Stillman, M. (1994): MACAULAY: A System for Computing in Algebraic Geometry and Commutative Algebra, Source and object code available for Unix and Macintosh computers. Contact the authors, or download from zariski.harvard.edu/Macaulay via anonymous ftp.
3. Buchsbaum, D. and Eisenbud, D. (1977): Algebraic structures for finite free resolutions and some structure theorems for ideals of codimension 3, Amer. J. Math. 99, 447-485.
4. Burnside, W. (1911): Theory of Groups of Finite Order, Cambridge Univ. Press, Cambridge. Reprinted by Dover, New York.
5. Clebsch, A. (1861): Über Curven vierter Ordnung, J. Reine Angew. Math. 59, 125-145.
6. Dolgachev, I. and Kenev, V. (1993): Polar covariants of plane cubics and quartics, Adv. Math. 98, 216-301.
7. Eisenbud, D. (1995): Commutative Algebra with a View Toward Algebraic Geometry, Grad. Texts Math. 150, Springer-Verlag, New York.
8. Ellingsrud, G., Piene, R. and Strømme, S.-A. (1987): On the variety of nets of quadrics defining cubics, in Space Curves, Proceedings, Rocca di Papa 1985, Lecture Notes in Math. 1266, Springer, New York, pp. 84-96.
9. Fano, G. (1937): Sulle varietà algebriche a tre dimensioni a curve-sezioni canoniche, Mem. R. Acc. d'Italia 8, 23-64.
10. Hartshorne, R. (1977): Algebraic Geometry, Grad. Texts Math. 52, Springer-Verlag, New York, Heidelberg, Berlin.
11. Iarrobino, A. (1984): Compressed algebras: Artin algebras having socle degree and maximal length, Trans. Amer. Math. Soc. 285, 337-378.
12. Iarrobino, A. (1994): Associated graded algebra of a Gorenstein Artin algebra, Mem. Amer. Math. Soc., 514.
13. Iarrobino, A. (1995): Inverse systems of a symbolic power. II: The Waring problem for forms, J. Algebra 174, 1091-1110.
14. Iarrobino, A. and Kanev, V. (1999): Power Sums, Gorenstein Algebras, and Determinantal Loci. With an appendix: The Gotszmann Theorems and the Hilbert Scheme by Anthony Iarrobino and Steven L. Kleiman. Lecture Notes in Math. 1721, Springer, Berlin.
15. Macaulay, F. S. (1916): Algebraic Theory of Modular Systems, Cambridge Univ. Press, London.
16. Mukai, S. (1992): Fano 3-folds, in: Complex Projective Geometry, London Math. Soc. Lecture Notes Ser. 179, Cambridge University Press, 255-263.
17. Mukai, S. (1995): Curves and symmetric spaces I, Amer. J. Math. 117, 1627-1644.
18. Mukai, S. and Umemura, H. (1983): Minimal rational 3-folds, in: Algebraic Geometry, Proceedings Tokyo, Kyoto 1982, Lecture Notes in Math. 1016, Springer, New York, pp. 490-518.
19. Okonek, C., Schneider, M. and Spindler, H. (1980): Vector Bundles on Complex Projective Spaces, Birkäuser, Boston.
20. Piene, R. and Schlessinger, M. (1985): On the Hilbert scheme compactification of the space of twisted cubics, Amer. J. Math. 107, 761-774.
21. Rosanes, J. (1873): Über ein Prinzip der Zuordnung algebraischer Formen, J. Reine Angew. Math. 76, 312-330.
22. Salmon, G. (1885): Modern Higher Algebra, 4th edn., Hodges, Figgis, and Co., Dublin.
23. Schreyer, F.-O. (1991): A standard basis approach to syzygies of canonical curves, J. Reine Angew. Math. 421, 81-123.
24. Scorza, G. (1899): Sopra la teoria delle figure polari delle curve piane del 4. ordine, Ann. di Mat. (3) 2, 155-202.
25. Scorza, G. (1899): Un nuovo theorema sopra le quartiche piane generali, Math. Ann. 52, 457-461.
26. Sylvester, J. J. (1904): Sketch of a memoir on elimination, transformation and canonical forms, Collected Works, Vol. I, Cambridge Univ. Press, pp. 184-197.
27. Sylvester, J. J. (1904): An Essay on Canonical Forms, Supplemented by a Sketch of a Memoir on Elimination, Transformation and Canonical Forms, Collected Works, Vol. I, Cambridge Univ. Press, 203-216.
28. Sylvester, J. J. (1886): Sur une extension d'un théorème de Clebsch relatif aux courbes de quartième degré, C. R. Acad. Sci. 102, 1532-1534 (Collected Math. Works IV, 527-530).
29. Sylvester, J. J. (1886): Sur une extension d'un théorème de Clebsch relatif aux courbes de quartième degré, C. R. Acad. Sci. 102, 1532-1534 (Collected Math. Works IV, 527-530).