Gauss-Manin System and the Virtual Structure Constants
arXiv:math/0109039 · doi:10.1142/S0129167X02001368
Abstract
In this paper, we discuss some applications of Givental's differential equations to enumerative problems on rational curves in projective hypersurfaces. Using this method, we prove some of the conjectures on the structure constants of quantum cohomology of projective hypersurfaces, proposed in our previous article. Moreover, we clarify the correspondence between the virtual structure constants and Givental's differential equations when the projective hypersurface is Calabi-Yau or general type.
25 pages, Latex, references added, minor errors are corrected
References in corpus (4)
- Generalized periods and mirror symmetry in dimensions n>3
- On the Quantum Cohomology Rings of General Type Projective Hypersurfaces and Generalized Mirror Transformation
- Completion of the Conjecture: Quantum Cohomology of Fano Hypersurfaces
- Virtual Gromov-Witten Invariants and the Quantum Cohomology Rings of General Type Projective Hypersurfaces
Cited by in corpus (5)
- Mirror Map as Generating Function of Intersection Numbers: Toric Manifolds with Two Kähler Forms
- Open Virtual Structure Constants and Mirror Computation of Open Gromov-Witten Invariants of Projective Hypersurfaces
- Geometrical Proof of Generalized Mirror Transformation of Projective Hypersurfaces
- Direct Proof of Mirror Theorem of Projective Hypersurfaces up to degree 3 Rational Curves
- Coordinate Change of Gauss-Manin System and Generalized Mirror Transformation