A Taylor Resolution Over Complete Intersections

TL;DR

This paper extends the classical Taylor resolution, a key tool in algebraic geometry, to complete intersection rings using the Eisenbud--Shamash construction, broadening its applicability.

Contribution

It introduces a generalized Taylor resolution for complete intersections, expanding the scope of the classical construction through the Eisenbud--Shamash method.

Findings

Provides an explicit construction of the resolution over complete intersections.

Demonstrates the applicability of the generalized resolution to a broader class of rings.

Enhances understanding of free resolutions in algebraic geometry.

Abstract

The Taylor resolution is a fundamental object in the study of free resolutions over the polynomial ring, due to its explicit formula, cellular/combinatorial structure, and applicability to any and all monomial ideals. This paper generalizes the Taylor resolution to complete intersection rings via the Eisenbud--Shamash construction.