Work

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

Year: 2026

Type: article

Abstract: In this paper, we develop a framework that allows one to describe the birational geometry of Calabi–Yau pairs ( X , D ) (X,D) . After establishing some general results for ( X , D ) (X,D) with mild singularities, we focus on the special case when X = P 3 X=\mathbb{P}^{3} and D ⊂ P 3 D\subset\mathbb{P}^{3} is a quartic surface. We investigate how the appearance of increasingly worse singularities in 𝐷 enriches the birational geometry of the pair ( P 3 , D ) (\mathbb{P}^{3},D) , and leads to interesting subgroups of the Cremona group of P 3 \mathbb{P}^{3} .

Source: Journal für die reine und angewandte Mathematik (Crelles Journal)

DOI: 10.1515/crelle-2025-0095

Authors: Carolina Araujo, Alessio Corti, Alex Massarenti

Institutions: Instituto Nacional de Matemática Pura e Aplicada, Imperial College London, University of Ferrara

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Engineering and Physical Sciences Research Council

Award: Classification, Computation, and Construction: New Methods in Geometry