The quadratic Euler characteristic of a smooth projective same-degree complete intersection

TL;DR

This paper presents an algorithm for computing the quadratic Euler characteristic of smooth projective complete intersections of same-degree hypersurfaces, with explicit calculations for generalized Fermat hypersurfaces, advancing algebraic geometry methods.

Contribution

It introduces a novel algorithm for calculating the quadratic Euler characteristic in specific algebraic varieties, expanding computational tools in algebraic geometry.

Findings

Algorithm successfully computes quadratic Euler characteristics

Explicit example for generalized Fermat hypersurfaces

Contributes to algebraic geometry computational methods

Abstract

We find an algorithm to compute the quadratic Euler characteristic of a smooth projective complete intersection of hypersurfaces of the same degree. As an example, we compute the quadratic Euler characteristic of a smooth projective complete intersection of two generalized Fermat hypersurfaces. The results presented here also form a chapter in the author's thesis, which was submitted on May 30'th, 2023.