On quadratically enriched excess and residual intersections

TL;DR

This paper develops new tools based on duality results to study quadratically enriched residual intersections and derives a formula for the Witt-valued Euler number of almost complete intersections, supported by example computations.

Contribution

It introduces a novel approach using Eisenbud--Ulrich duality to analyze quadratically enriched residual intersections without excess bundles, and provides a formula for the Witt-valued Euler number.

Findings

Derived a formula for the Witt-valued Euler number of almost complete intersections

Provided example computations of quadratically enriched residual intersections

Developed tools for studying residual intersections using duality

Abstract

We use recent duality results of Eisenbud--Ulrich to give tools to study quadratically enriched residual intersections when there is no excess bundle. We use this to prove a formula for the Witt-valued Euler number of an almost complete intersection. We give example computations of quadratically enriched excess and residual intersections.