A degeneration of stable morphisms and relative stable morphisms

Jun Li

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arXiv · math/0009097

A degeneration of stable morphisms and relative stable morphisms

Jun Li

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Abstract

The introduction is modified in the revised version. Also, many typos and errors were corrected. Let $W\to C$ be degeneration of smooth varieties so that the special fiber has normal crossing singularity. In this paper, we first constructed the stack of expanded degenerations of $W$. We then constructed the moduli space of stable morphisms to this stack, which provides a degeneration of the moduli spaces of stable morphisms associated to $W/C$. Using similar technique, for a pair of smooth variety and a smooth divisor $(Z,D)$, we constructed the stack of expanded relative pairs and then the moduli spaces of relative stable morphisms to $(Z,D)$. In the subsequent paper we will construct the relative Gromov-Witten invariants and prove a degeneration formula of Gromov-Witten invariants.

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Jun Li. 2001-04-15. A degeneration of stable morphisms and relative stable morphisms. https://arxiv.org/abs/math/0009097

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