메뉴 건너뛰기




Volumn 9, Issue 1, 1996, Pages 175-193

Bott's formula and enumerative geometry

Author keywords

Bott's residue formula; Complete intersection; Darboux curve; Gromov witten number; Ternary power sum; Torus action; Twisted cubic

Indexed keywords


EID: 0030545478     PISSN: 08940347     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0894-0347-96-00189-0     Document Type: Article
Times cited : (60)

References (57)
  • 2
    • 0001387877 scopus 로고    scopus 로고
    • 1, J. Reine Angew. Math. 445 (1993), 205-220. MR 94j:14044
    • MR , vol.94 J , pp. 14044
  • 3
    • 0009781709 scopus 로고    scopus 로고
    • The moment map and equivariant cohomology
    • M. Atiyah and R. Bott, The moment map and equivariant cohomology, Topology 23 (1984), 1-28. MR 85e:58041
    • (1984) Topology , vol.23 , pp. 1-28
    • Atiyah, M.1    Bott, R.2
  • 4
    • 0009781709 scopus 로고    scopus 로고
    • M. Atiyah and R. Bott, The moment map and equivariant cohomology, Topology 23 (1984), 1-28. MR 85e:58041
    • MR , vol.85 E , pp. 58041
  • 6
    • 0347613042 scopus 로고    scopus 로고
    • D. Avritzer and I. Vainsencher, Compactifying the space of elliptic quartic curves, in Ellingsrud et al. [12], pp. 47-58. MR 93g:14002
    • MR , vol.93 G , pp. 14002
  • 7
    • 34250301396 scopus 로고    scopus 로고
    • Moduli of vector bundles on the projective plane
    • W. Barth, Moduli of vector bundles on the projective plane, Invent. Math. 42 (1977), 63-91. MR 57:324
    • (1977) Invent. Math. , vol.42 , pp. 63-91
    • Barth, W.1
  • 8
    • 34250301396 scopus 로고    scopus 로고
    • W. Barth, Moduli of vector bundles on the projective plane, Invent. Math. 42 (1977), 63-91. MR 57:324
    • MR , vol.57 , pp. 324
  • 9
    • 0001461387 scopus 로고
    • Holomorphic anomalies in topological field theories
    • M. Bershadsky, S. Cecotti, H. Ooguri, and C. Vafa, Holomorphic anomalies in topological field theories, Nuclear Phys. B 407 (1993), 667-705. MR 94j:81254
    • (1993) Nuclear Phys. B , vol.407 , pp. 667-705
    • Bershadsky, M.1    Cecotti, S.2    Ooguri, H.3    Vafa, C.4
  • 10
    • 0348242877 scopus 로고    scopus 로고
    • M. Bershadsky, S. Cecotti, H. Ooguri, and C. Vafa, Holomorphic anomalies in topological field theories, Nuclear Phys. B 407 (1993), 667-705. MR 94j:81254
    • MR , vol.94 J , pp. 81254
  • 11
    • 84972494458 scopus 로고    scopus 로고
    • A residue formula for holomorphic vector fields
    • R. Bott, A residue formula for holomorphic vector fields, J. Differential Geom. 1 (1967), 311-330. MR 38:730
    • (1967) J. Differential Geom. , vol.1 , pp. 311-330
    • Bott, R.1
  • 12
    • 84972494458 scopus 로고    scopus 로고
    • R. Bott, A residue formula for holomorphic vector fields, J. Differential Geom. 1 (1967), 311-330. MR 38:730
    • MR , vol.38 , pp. 730
  • 13
    • 0002925364 scopus 로고    scopus 로고
    • A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory
    • P. Candelas, P. S. Green, X. C. de la Ossa, and L. Parkes, A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory, Nuclear Phys. B 359 (1991), 21-74. MR 93b:32029
    • (1991) Nuclear Phys. B , vol.359 , pp. 21-74
    • Candelas, P.1    Green, P.S.2    De La Ossa, X.C.3    Parkes, L.4
  • 14
    • 0002925364 scopus 로고    scopus 로고
    • P. Candelas, P. S. Green, X. C. de la Ossa, and L. Parkes, A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory, Nuclear Phys. B 359 (1991), 21-74. MR 93b:32029
    • MR , vol.93 B , pp. 32029
  • 15
    • 0000671087 scopus 로고    scopus 로고
    • Holomorphic vector fields and Kaehler manifolds
    • J. B. Carrell and D. I. Lieberman, Holomorphic vector fields and Kaehler manifolds, Invent. Math. 21 (1973), 303-309. MR 48:4356
    • (1973) Invent. Math. , vol.21 , pp. 303-309
    • Carrell, J.B.1    Lieberman, D.I.2
  • 16
    • 0000671087 scopus 로고    scopus 로고
    • J. B. Carrell and D. I. Lieberman, Holomorphic vector fields and Kaehler manifolds, Invent. Math. 21 (1973), 303-309. MR 48:4356
    • MR , vol.48 , pp. 4356
  • 17
    • 0013482799 scopus 로고    scopus 로고
    • Vector fields and Chern numbers
    • _, Vector fields and Chern numbers, Math. Ann. 225 (1977), 263-273. MR 55:8416
    • (1977) Math. Ann. , vol.225 , pp. 263-273
  • 18
    • 0013482799 scopus 로고    scopus 로고
    • _, Vector fields and Chern numbers, Math. Ann. 225 (1977), 263-273. MR 55:8416
    • MR , vol.55 , pp. 8416
  • 20
    • 0040451148 scopus 로고
    • Über curven vierter ordnung
    • A. Clebsch, Über Curven vierter Ordnung, J. Reine Angew. Math. 59 (1861), 125-145.
    • (1861) J. Reine Angew. Math. , vol.59 , pp. 125-145
    • Clebsch, A.1
  • 22
    • 0347613042 scopus 로고    scopus 로고
    • G. Ellingsrud, C. Peskine, G. Sacchiero, and S. A. Strømme, editors, Complex algebraic geometry, London Math. Soc. Lecture Note Series, vol. 179, Cambridge Univ. Press, London and New York, 1992. MR 93g:14002
    • MR , vol.93 G , pp. 14002
  • 23
    • 0002596323 scopus 로고
    • On the variety of nets of quadrics defining twisted cubic curves
    • Space Curves (Franco Ghione, Christian Peskine, and Eduardo Sernesi, eds.), Springer-Verlag, Berlin, Heidelberg, and New York
    • G. Ellingsrud, R. Piene, and S. A. Strømme, On the variety of nets of quadrics defining twisted cubic curves, Space Curves (Franco Ghione, Christian Peskine, and Eduardo Sernesi, eds.), Lecture Notes in Math., vol. 1266, Springer-Verlag, Berlin, Heidelberg, and New York, 1987. MR 88h:14034
    • (1987) Lecture Notes in Math. , vol.1266
    • Ellingsrud, G.1    Piene, R.2    Strømme, S.A.3
  • 24
    • 0346352164 scopus 로고    scopus 로고
    • G. Ellingsrud, R. Piene, and S. A. Strømme, On the variety of nets of quadrics defining twisted cubic curves, Space Curves (Franco Ghione, Christian Peskine, and Eduardo Sernesi, eds.), Lecture Notes in Math., vol. 1266, Springer-Verlag, Berlin, Heidelberg, and New York, 1987. MR 88h:14034
    • MR , vol.88 H , pp. 14034
  • 25
    • 0000302452 scopus 로고    scopus 로고
    • On the homology of the Hilbert scheme of points in the plane
    • G. Ellingsrud and S. A. Strømme, On the homology of the Hilbert scheme of points in the plane, Invent. Math. 87 (1987), 343-352. MR 88c:14008
    • (1987) Invent. Math. , vol.87 , pp. 343-352
    • Ellingsrud, G.1    Strømme, S.A.2
  • 26
    • 0000302452 scopus 로고    scopus 로고
    • G. Ellingsrud and S. A. Strømme, On the homology of the Hilbert scheme of points in the plane, Invent. Math. 87 (1987), 343-352. MR 88c:14008
    • MR , vol.88 C , pp. 14008
  • 27
    • 0003057798 scopus 로고    scopus 로고
    • 2
    • 2, J. Reine Angew. Math. 441 (1993), 33-44. MR 94i:14004
    • (1993) J. Reine Angew. Math. , vol.441 , pp. 33-44
  • 28
    • 0003057798 scopus 로고    scopus 로고
    • 2, J. Reine Angew. Math. 441 (1993), 33-44. MR 94i:14004
    • MR , vol.94 I , pp. 14004
  • 29
    • 0346982015 scopus 로고
    • The number of twisted cubic curves on the general quintic threefold
    • _, The number of twisted cubic curves on the general quintic threefold, Math. Scand. 76 (1995).
    • (1995) Math. Scand. , vol.76
  • 30
    • 0000975014 scopus 로고
    • Algebraic families on an algebraic surface
    • J. Fogarty, Algebraic families on an algebraic surface, Amer. J. Math. 90 (1968), 511-521. MR 38:5778
    • (1968) Amer. J. Math. , vol.90 , pp. 511-521
    • Fogarty, J.1
  • 31
    • 0039205553 scopus 로고    scopus 로고
    • J. Fogarty, Algebraic families on an algebraic surface, Amer. J. Math. 90 (1968), 511-521. MR 38:5778
    • MR , vol.38 , pp. 5778
  • 32
    • 0003314349 scopus 로고
    • Intersection theory
    • Springer-Verlag, Berlin, Heidelberg, and New York
    • W. Fulton, Intersection theory, Ergeb. Math. Grenzgebiete, vol. 2, Springer-Verlag, Berlin, Heidelberg, and New York, 1984. MR 85k:14004
    • (1984) Ergeb. Math. Grenzgebiete , vol.2
    • Fulton, W.1
  • 33
    • 0039236455 scopus 로고    scopus 로고
    • W. Fulton, Intersection theory, Ergeb. Math. Grenzgebiete, vol. 2, Springer-Verlag, Berlin, Heidelberg, and New York, 1984. MR 85k:14004
    • MR , vol.85 K , pp. 14004
  • 35
    • 0003322387 scopus 로고
    • Algebraic geometry
    • Springer-Verlag, Berlin, Tokyo, and New York
    • R. Hartshorne, Algebraic geometry, Graduate Texts in Math., no. 52, Springer-Verlag, Berlin, Tokyo, and New York, 1977. MR 57:3116
    • (1977) Graduate Texts in Math. , vol.52
    • Hartshorne, R.1
  • 36
    • 0039995436 scopus 로고    scopus 로고
    • R. Hartshorne, Algebraic geometry, Graduate Texts in Math., no. 52, Springer-Verlag, Berlin, Tokyo, and New York, 1977. MR 57:3116
    • MR , vol.57 , pp. 3116
  • 37
    • 0346982020 scopus 로고
    • Rational curves on Calabi-Yau manifolds: Verifying predictions of mirror symmetry
    • E. Ballico, ed., Marcel-Dekker, New York
    • S. Katz, Rational curves on Calabi-Yau manifolds: Verifying predictions of Mirror Symmetry, Algebraic Geometry (E. Ballico, ed.), Marcel-Dekker, New York, 1994. CMP 95:04
    • (1994) Algebraic Geometry
    • Katz, S.1
  • 38
    • 25344463146 scopus 로고    scopus 로고
    • S. Katz, Rational curves on Calabi-Yau manifolds: Verifying predictions of Mirror Symmetry, Algebraic Geometry (E. Ballico, ed.), Marcel-Dekker, New York, 1994. CMP 95:04
    • CMP , vol.95 , pp. 04
  • 40
    • 0001274052 scopus 로고
    • The transversality of a general translate
    • S. L. Kleiman, The transversality of a general translate, Compositio Math. 28 (1974), 287-297. MR 50:13063
    • (1974) Compositio Math. , vol.28 , pp. 287-297
    • Kleiman, S.L.1
  • 41
    • 0346352160 scopus 로고    scopus 로고
    • S. L. Kleiman, The transversality of a general translate, Compositio Math. 28 (1974), 287-297. MR 50:13063
    • MR , vol.50 , pp. 13063
  • 43
    • 34249763252 scopus 로고    scopus 로고
    • Gromov-Witten classes, quantum cohomology, and enumerative geometry
    • M. Kontsevich and Y. Manin, Gromov-Witten classes, quantum cohomology, and enumerative geometry, Comm. Math. Phys. 164 (1994), 525-562. CMP 94:17
    • (1994) Comm. Math. Phys. , vol.164 , pp. 525-562
    • Kontsevich, M.1    Manin, Y.2
  • 44
    • 34249763252 scopus 로고    scopus 로고
    • M. Kontsevich and Y. Manin, Gromov-Witten classes, quantum cohomology, and enumerative geometry, Comm. Math. Phys. 164 (1994), 525-562. CMP 94:17
    • CMP , vol.94 , pp. 17
  • 46
    • 0002537653 scopus 로고
    • Lines on Calabi Yau complete intersections, mirror symmetry, and Picard Fuchs equations
    • International Mathematics Research Notes 1993, No. 1
    • A. Libgober and J. Teitelbaum, Lines on Calabi Yau complete intersections, mirror symmetry, and Picard Fuchs equations, Duke Math. J. 69 (1993), 29-39. International Mathematics Research Notes 1993, No. 1. MR 93k:14013
    • (1993) Duke Math. J. , vol.69 , pp. 29-39
    • Libgober, A.1    Teitelbaum, J.2
  • 47
    • 0347613038 scopus 로고    scopus 로고
    • A. Libgober and J. Teitelbaum, Lines on Calabi Yau complete intersections, mirror symmetry, and Picard Fuchs equations, Duke Math. J. 69 (1993), 29-39. International Mathematics Research Notes 1993, No. 1. MR 93k:14013
    • MR , vol.93 K , pp. 14013
  • 49
    • 0042198487 scopus 로고
    • On the lüroth quartic curve
    • F. Morley, On the Lüroth quartic curve, Amer. J. Math. 36 (1918).
    • (1918) Amer. J. Math. , vol.36
    • Morley, F.1
  • 50
    • 25344436735 scopus 로고    scopus 로고
    • Ellingsrud et al. [12]
    • S. Mukai, Fano 3-folds, in Ellingsrud et al. [12], pp. 255-263. MR 94a:14042
    • Fano 3-folds , pp. 255-263
    • Mukai, S.1
  • 51
    • 0346982016 scopus 로고    scopus 로고
    • S. Mukai, Fano 3-folds, in Ellingsrud et al. [12], pp. 255-263. MR 94a:14042
    • MR , vol.94 A , pp. 14042
  • 52
    • 0001668422 scopus 로고
    • On the Hilbert scheme compactification of the space of twisted cubics
    • R. Piene and M. Schlessinger, On the Hilbert scheme compactification of the space of twisted cubics, Amer. J. Math. 107 (1985), 761-774. MR 86m:14004
    • (1985) Amer. J. Math. , vol.107 , pp. 761-774
    • Piene, R.1    Schlessinger, M.2
  • 53
    • 0348242872 scopus 로고    scopus 로고
    • R. Piene and M. Schlessinger, On the Hilbert scheme compactification of the space of twisted cubics, Amer. J. Math. 107 (1985), 761-774. MR 86m:14004
    • MR , vol.86 M , pp. 14004


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.