Configurations of points with sum 0

TL;DR

This paper calculates the virtual Poincaré polynomials for the space of n ordered points on an elliptic curve whose sum is zero, providing insights into the topological structure of these configurations.

Contribution

It introduces explicit computations of the virtual Poincaré polynomials for these specific configuration spaces, a novel contribution in algebraic geometry.

Findings

Explicit formulas for the virtual Poincaré polynomials

Enhanced understanding of the topology of point configurations on elliptic curves

New methods for computing invariants of configuration spaces

Abstract

We compute the virtual Poincar\'e polynomials of the configuration space of $n$ ordered points on an elliptic curve with sum 0.