First order deformations of schemes with normal crossing singularities

TL;DR

This paper provides a detailed description of the sheaf T^1(X) that governs first order deformations of schemes with normal crossing singularities, including a formula in a log resolution.

Contribution

It introduces a formula for T^1(X) in a log resolution, advancing understanding of deformations of schemes with normal crossing singularities.

Findings

Derived a formula for T^1(X) in a log resolution

Described the sheaf T^1(X) for schemes with normal crossing singularities

Enhanced the understanding of first order deformations in algebraic geometry

Abstract

We describe the sheaf T^1(X) of first order deformations of a reduced scheme with normal crossing singularities. In particular, we obtain a formula for T^1(X) in a suitable log resolution of X.