Birational geometry of Calabi-Yau pairs and 3-dimensional Cremona transformations

Author:

Carolina Araujo, Alessio Corti, Alex Massarenti

Keyword:

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

journal:

date:

2023-05-30 16:00:00

Abstract

We develop a framework that allows one to describe the birational geometry of Calabi-Yau pairs $(X,D)$. After establishing some general results for Calabi-Yau pairs $(X,D)$ with mild singularities, we focus on the special case when $X=\mathbb{P}^3$ and $D\subset \mathbb{P}^3$ is a quartic surface. We investigate how the appearance of increasingly worse singularities on $D$ enriches the birational geometry of the pair $(\mathbb{P}^3, D)$.

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