On Punctual Quot Schemes for Algebraic Surfaces

TL;DR

This paper studies the punctual Quot scheme for algebraic surfaces, proving its irreducibility and specific dimension, which advances understanding of the structure of these schemes in algebraic geometry.

Contribution

The paper establishes the irreducibility and dimension of punctual Quot schemes for algebraic surfaces, providing a key structural result in the field.

Findings

The punctual Quot scheme is irreducible.

Its dimension is (rd-1).

The result was independently confirmed by Ellingsrud and Lehn.

Abstract

The punctual Quot scheme parametrizes all length d quotients of a (locally) trivial rank r sheaf which are supported at a fixed point. The author shows that this scheme is irreducible and (rd-1)-dimensional. The same result was proved independently by Ellingsrud and Lehn.