Frobenius Manifolds And Virasoro Constraints
Boris Dubrovin, Youjin Zhang
TL;DR
This paper constructs Virasoro constraints for Frobenius manifolds and proves their validity in genus one for semisimple cases, confirming conjectures for certain smooth projective varieties with semisimple quantum cohomology.
Contribution
It develops a system of Virasoro constraints applicable to any Frobenius manifold and proves these constraints in genus one for semisimple cases, confirming related conjectures.
Findings
Virasoro constraints are valid in genus one for semisimple Frobenius manifolds.
The genus ≤ 1 Virasoro conjecture is proved for smooth projective varieties with semisimple quantum cohomology.
A new system of Virasoro constraints is constructed for Frobenius manifolds.
Abstract
For an arbitrary Frobenius manifold a system of Virasoro constraints is constructed. In the semisimple case these constraints are proved to hold true in the genus one approximation. Particularly, the genus Virasoro conjecture of T.Eguchi, K.Hori, M.Jinzenji, and C.-S.Xiong and of S.Katz is proved for smooth projective varieties having semisimple quantum cohomology.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Nonlinear Waves and Solitons · Homotopy and Cohomology in Algebraic Topology