Constructing smoothings of stable maps

Author:

Fatemeh Rezaee, Mohan Swaminathan

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Symplectic Geometry (math.SG)

journal:

date:

2023-09-21 16:00:00

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.

PDF: Constructing smoothings of stable maps.pdf