Elliptic Gromov-Witten Invariants And Virasoro Conjecture

摘要

The Virasoro conjecture proposed by Eguchi-Hori-Xiong and S. Katz predictsthat the generating function of Gromov-Witten invariants is annihilated byinfinitely many differential operators which form a half branch of the Virasoroalgebra. In this paper, we study the genus-1 case of the conjecture. Inparticular, we will give some necessary and sufficient conditions for thegenus-1 Virasoro conjecture.