Equivariant cobordism of smooth projective spherical varieties

TL;DR

This paper investigates the structure of equivariant cobordism rings for smooth projective spherical varieties under torus actions, providing explicit descriptions and presentations, especially for horospherical varieties of Picard number one.

Contribution

It establishes a theorem describing the rational equivariant cobordism rings of smooth projective G-spherical varieties with torus action, and derives explicit presentations for specific horospherical cases.

Findings

Rational T-equivariant cobordism rings are explicitly described for smooth projective G-spherical varieties.

Explicit presentations are obtained for horospherical varieties of Picard number one.

The results facilitate computations of cobordism rings in algebraic geometry.

Abstract

We study the equivariant cobordism rings for the action of a torus $T$ on smooth varieties over an algebraically closed field of characteristic zero. We prove a theorem describing the rational $T$-equivariant cobordism rings of smooth projective $G$-spherical varieties with the action of a maximal torus $T$ of $G$. As an application, we obtain explicit presentations for the rational equivariant cobordism rings of smooth projective horospherical varieties of Picard number one.