On the degree of Fano schemes of linear subspaces on hypersurfaces

TL;DR

This paper derives an explicit formula for calculating the degree of Fano schemes of linear subspaces on hypersurfaces using localization and Bott's residue formula, advancing algebraic geometry tools.

Contribution

It introduces a new explicit formula for the degree of Fano schemes on hypersurfaces, utilizing equivariant intersection theory methods.

Findings

Derived an explicit degree formula for Fano schemes

Applied localization theorem and Bott's residue formula

Enhanced computational techniques in algebraic geometry

Abstract

In this paper we propose and prove an explicit formula for computing the degree of Fano schemes of linear subspaces on general hypersurfaces. The method used here is based on the localization theorem and Bott's residue formula in equivariant intersection theory.