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arXiv · 2309.12936

Constructing smoothings of stable maps

Fatemeh Rezaee·Mohan Swaminathan
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Abstract

Let $X$ be a smooth projective variety. Define a stable map $f:C\to X$ to be "eventually smoothable" if there is an embedding $X\hookrightarrow\mathbb{P}^N$ such that $(C,f)$ occurs as the limit of a $1$-parameter family of stable maps to $\mathbb{P}^N$ with smooth domain curves. Via an explicit deformation-theoretic construction, we produce a large class of stable maps (called "stable maps with model ghosts"), and show that they are eventually smoothable.

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Fatemeh Rezaee, Mohan Swaminathan. 2023-09-22. Constructing smoothings of stable maps. https://arxiv.org/abs/2309.12936

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