The Euler number of a $C^*$-invariant subvariety in $P^n$

TL;DR

This paper proves that the Euler number of a $C^*$-equivariantly embedded projective variety in $P^n$ is bounded by $n+1$, confirming a conjecture by Carrell and Sommese.

Contribution

It establishes an upper bound for the Euler number of $C^*$-invariant subvarieties in projective space, confirming a previously conjectured bound.

Findings

Euler number of $C^*$-invariant subvarieties is bounded by $n+1$

Confirms Carrell and Sommese's conjecture

Provides a key inequality for equivariant embeddings

Abstract

In this note we show that the Euler number of a projective variety $C^*$-equivariantly embedded into a projective space $P^n$ is bounded by $n+1$, as conjectured by Carrell and Sommese.