K-theory, local cohomology and tangent spaces to Hilbert schemes

TL;DR

This paper uses K-theory to relate tangent spaces of Hilbert schemes to local cohomology, providing an affirmative answer to a question about tangent space mappings to cycle groups.

Contribution

It constructs a new map from the tangent space of the Hilbert scheme to local cohomology and addresses a question by Green and Griffiths about tangent space mappings.

Findings

Established a map from tangent space to local cohomology

Provided an affirmative answer to Green and Griffiths' question

Connected K-theory with tangent space structures in algebraic geometry

Abstract

By using K-theory, we construct a map from the tangent space to the Hilbert scheme at a point Y to the local cohomology group. And we use this map to answer affirmatively(after slight modification) a question by Mark Green and Phillip Griffiths in [8] on constructing a map from the tangent space to the Hilbert scheme to the tangent space to the cycle group.