Reduced genus-one Gromov-Witten invariants

作者: Aleksey Zinger

DOI: 10.4310/JDG/1261495337

关键词: Modular equationModuli spaceMathematicsModuli of algebraic curvesPseudoholomorphic curveAlgebraSymplectic manifoldPure mathematicsGeometric invariant theoryGromov–Witten invariantSymplectic geometryGeometry and topologyAlgebra and Number TheoryAnalysis

摘要: In a previous paper we described natural closed subset M 0 1,k(X,A; J) of the moduli space M1,k(X,A; stable genus-one J-holomorphic maps into symplectic manifold X. this generalize definition main component to spaces perturbed, in restricted way, maps. This generalization implies that J), just like carries virtual fundamental class and can be used define invariants. These truly invariants constitute part standard GromovWitten invariants, which arise from entire J). The new are more geometric compute GW-invariants complete intersections, as shown separate paper.

参考文章(20)
Aleksey Zinger, Enumeration of Genus-Two Curves with a Fixed Complex Structure in ℙ 2 and ℙ 3 Journal of Differential Geometry. ,vol. 65, pp. 341- 467 ,(2003) , 10.4310/JDG/1090511749
Andreas Floer, Helmut Hofer, Dietmar Salamon, Transversality in elliptic Morse theory for the symplectic action Duke Mathematical Journal. ,vol. 80, pp. 251- 292 ,(1995) , 10.1215/S0012-7094-95-08010-7
Jun Li, Aleksey Zinger, On the genus-one Gromov-Witten invariants of complete intersections Journal of Differential Geometry. ,vol. 82, pp. 641- 690 ,(2009) , 10.4310/JDG/1251122549
Yongbin Ruan, Gang Tian, A mathematical theory of quantum cohomology Journal of Differential Geometry. ,vol. 42, pp. 259- 367 ,(1995) , 10.4310/JDG/1214457234
Michael Bershadsky, Sergio Cecotti, Hirosi Ooguri, Cumrun Vafa, None, Holomorphic anomalies in topological field theories Nuclear Physics. ,vol. 405, pp. 279- 304 ,(1993) , 10.1016/0550-3213(93)90548-4
Aleksey Zinger, The reduced genus 1 Gromov-Witten invariants of Calabi-Yau hypersurfaces Journal of the American Mathematical Society. ,vol. 22, pp. 691- 737 ,(2008) , 10.1090/S0894-0347-08-00625-5
Aleksey Zinger, Enumerative vs.\ symplectic invariants and obstruction bundles Journal of Symplectic Geometry. ,vol. 2, pp. 445- 543 ,(2004) , 10.4310/JSG.2004.V2.N4.A1
R. Pandharipande, Hodge Integrals and Degenerate Contributions Communications in Mathematical Physics. ,vol. 208, pp. 489- 506 ,(1999) , 10.1007/S002200050766
Kenji Fukaya, Kaoru Ono, ARNOLD CONJECTURE AND GROMOV–WITTEN INVARIANT Topology. ,vol. 38, pp. 933- 1048 ,(1999) , 10.1016/S0040-9383(98)00042-1
Ravi Vakil, Aleksey Zinger, A natural smooth compactification of the space of elliptic curves in projective space Electronic Research Announcements of The American Mathematical Society. ,vol. 13, pp. 53- 59 ,(2007) , 10.1090/S1079-6762-07-00174-6