Explicit Orbifold Riemann-Roch for quasismooth varieties

TL;DR

This paper develops a Riemann-Roch formula for quasismooth varieties viewed as quotient stacks and provides a parsing formula for Hilbert series of certain Gorenstein varieties with orbifold features.

Contribution

It introduces an explicit Riemann-Roch formula for quasismooth varieties as quotient stacks and extends Hilbert series parsing to include orbifold curves and dissident points.

Findings

Derived a Riemann-Roch formula for quasismooth varieties as quotient stacks

Extended Hilbert series parsing to varieties with orbifold curves and dissident points

Provides a new computational tool for Gorenstein algebraic varieties

Abstract

Considering quasismooth varieities as global $\CC^*$ quotients, we present a Riemann-Roch formula via general Riemann-Roch formula for quotient stacks. Furthermore, we give a parcing formula for Hilbert series associated to a polarized quasismooth projectively Gorenstein algebraic varieties with orbifold curves and dissident points, which is an extension of the result in \cite{BRZ}.