Excess dimension for secant loci in symmetric products of curves

TL;DR

This paper extends a classical result to secant loci in symmetric products of curves, showing that larger loci do not have excessively greater dimensions than smaller ones, thus providing bounds on their dimensions.

Contribution

It introduces a comparison of three secant loci in symmetric products of curves and establishes bounds on their dimensions, extending previous foundational work.

Findings

Dimensions of larger secant loci are not excessively larger than smaller ones

Comparison of three secant loci in symmetric products

Extension of classical results by Fulton, Harris, and Lazarsfeld

Abstract

We extend a result of W. Fulton, J. Harris and R. Lazarsfeld to secant loci in symmetric products of curves. We compare three secant loci and prove the the dimensions of bigger loci can not be excessively larger than the dimension of smaller loci.