The Hartogs phenomenon in almost homogeneous varieties

TL;DR

This paper investigates the Hartogs extension phenomenon in noncompact almost homogeneous algebraic varieties, establishing cohomological, weight, and colored fan criteria, especially for spherical varieties.

Contribution

It introduces new cohomological and combinatorial criteria for the Hartogs phenomenon in almost homogeneous and spherical varieties, advancing understanding of extension properties.

Findings

Cohomological criteria for Hartogs extension

Weight criteria for Hartogs phenomenon

Colored fan criterion for spherical varieties

Abstract

We study the Hartogs extension phenomenon in noncompact almost homogeneous algebraic varieties and we prove the cohomological and weight criteria for the Hartogs phenomenon. In the case of spherical varieties, we prove a criterion for the Hartogs phenomenon in terms of colored fans.