Lower degree curves in X3,3 (C) P2 × P2

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（11）
• 页码范围: 2309-2316
• 页数: 8页
• 语种: 英文

摘要

In this paper we study low-degree low-genus curves in a generic hypersurface X of degree (3,3) in P2 × P2.We prove that the genus 0 and genus 1 curves of degree up to (2,2) are smooth and rigid.We then use the multiple cover formula to compute the Gromov-Witten invariants of X of degree up to (2,2) and genus up to 2.This provides some initial conditions to determine the full genus 1 and genus 2 Gromov-Witten invariants via Bershadsky-Cecotti-Ooguri-Vafa's Feynman rule,which is expected to be proved in the near future.