Motivic classes of Quot-schemes on surfaces

TL;DR

This paper computes the motivic classes of Quot-schemes parametrizing zero-dimensional quotients of sheaves on smooth surfaces, providing algebraic invariants in the Grothendieck ring.

Contribution

It introduces a method to determine the motivic classes of Quot-schemes on surfaces, linking geometric structures to algebraic invariants.

Findings

Explicit formulas for motivic classes of Quot-schemes

Connections between Quot-schemes and algebraic invariants

Advancement in understanding the geometry of sheaves on surfaces

Abstract

Given a locally free coherent sheaf on a smooth algebraic surface, we consider the Quot-scheme parametrizing zero-dimensional quotients of the sheaf and find the corresponding motivic class in the Grothendieck ring of algebraic varieties.