Relative Gromov-Witten invariants of projective completions of vector bundles

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（7）
• 页码范围: 1429-1438
• 页数: 10页
• 语种: 英文

摘要

It was proved by Fan and Lee (2016) and Fan (2017) that the absolute Gromov-Witten invariants oftwo projective bundles P(Vi) → X are identified canonically when the total Chern classes c(V1) and c(V2) satisfyc(V1) =c(V2) for two bundles V1 and V2 over a smooth projective variety X.In this paper,we show that therelative Gromov-Witten invariants of (P(Vi(◎) O),P(Vi)),i =1,2 are identified canonically when c(V1) =c(V2),where P(Vi(◎) O) are the projective completions of the bundles Vi → X,and the projective bundles P(Vi) arethe exceptional divisors in P(Vi(◎)O).