What question did this study set out to answer?

The aim is to describe the birational geometry of Calabi–Yau pairs, focusing on mild singularities and their effects.

January 25, 2026

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

Key Points

The aim is to describe the birational geometry of Calabi–Yau pairs, focusing on mild singularities and their effects.
Developed a framework for birational geometry of pairs (X,D) with mild singularities.
Analyzed special cases where X is a projective space P^3 and D is a quartic surface.
Investigated the impacts of singularities on the birational properties of the pair (P^3,D).
Established general results for birational geometry under mild singularity conditions.
Showed that increasing singularities in D enrich the geometry of (P^3,D).
Identified interesting subgroups of the Cremona group associated with P^3.

Abstract

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=P^3 and D ⊂ P 3 D^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) (P^3, D), and leads to interesting subgroups of the Cremona group of P 3 P^3.

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

Key Points

Abstract

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