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arXiv · 1712.04121

On relative Gromov--Witten invariants of projective completions of vector bundles

Cheng-Yong Du
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Abstract

It was proved by Fan--Lee and Fan that the absolute Gromov--Witten invariants of two projective bundles $\mathbb P(V_i)\rightarrow X$ are identified canonically when the total Chern classes $c(V_1)=c(V_2)$ for two bundles $V_1$ and $V_2$ over a smooth projective variety $X$. In this note we show that for the two projective completions $\mathbb P(V_i\oplus\mathcal O)$ of $V_i$ and their infinity divisors $\mathbb P(V_i)$, the relative Gromov--Witten invariants of $(\mathbb P(V_i\oplus\mathcal O),\mathbb P(V_i))$ are identified canonically when $c(V_1)=c(V_2)$.

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Cheng-Yong Du. 2017-12-12. On relative Gromov--Witten invariants of projective completions of vector bundles. https://doi.org/10.1007/s11425-017-9219-8

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