## Doctoral Dissertations

Dissertations that have an embargo placed on them will not be available to anyone until the embargo expires.

#### Title

Equivariant smoothings of cusp singularities

#### Author ORCID Identifier

https://orcid.org/0000-0002-1609-6946

#### AccessType

Open Access Dissertation

dissertation

#### Degree Name

Doctor of Philosophy (PhD)

Mathematics

2021

September

Paul Hacking

#### Subject Categories

Algebraic Geometry

#### Abstract

Let $p \in X$ be the germ of a cusp singularity and let $\iota$ be an antisymplectic involution, that is an involution free on $X\setminus \{p\}$ and such that there exists a nowhere vanishing holomorphic 2-form $\Omega$ on $X\setminus \{p\}$ for which $\iota^*(\Omega)=-\Omega$. We prove that a sufficient condiition for such a singularity equipped with an antisymplectic involution to be equivariantly smoothable is the existence of a Looijenga (or anticanonical) pair $(Y,D)$ that admits an involution free on $Y\setminus D$ and that reverses the orientation of $D$.

#### DOI

https://doi.org/10.7275/23342899

COinS