Weierstrass models

TL;DR

This paper introduces a higher-dimensional generalization of Weierstrass models for elliptic K3 surfaces, demonstrating their role as compactifications of torsors and exploring applications in Kahler geometry of Lagrangian fibrations on symplectic manifolds.

Contribution

It defines higher-dimensional Weierstrass models, proves their uniqueness as torsor compactifications, and applies these concepts to Kahler geometry in symplectic manifolds.

Findings

Higher-dimensional Weierstrass models are compactifications of torsors.

Uniqueness of the models as torsor compactifications.

Application to Kahler geometry of Lagrangian fibrations.

Abstract

Elliptic K3 admit contraction to plane models, the Weierstrass models. We define a higher dimensional notion of Weierstrass models, show that they are compactification of torsors in a unique form, and propose an application to the kahler geometry of a class of lagrangian fibrations on irreducible symplectic manifolds.