A Degeneration of Stable Morphisms and Relative Stable Morphisms
نویسنده
چکیده
Let W → 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.
منابع مشابه
Stable Morphisms to Singular Schemes and Relative Stable Morphisms
Let W/C be a degeneration of smooth varieties so that the special fiber has normal crossing singularity. In this paper, we first construct the stack of expanded degenerations of W . We then construct 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 a similar technique, for a pair (Z,D) of smooth v...
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