Curves in projective space and RSK

TL;DR

This paper connects geometric invariants of algebraic curves in projective space with combinatorial objects via the RSK correspondence, providing a new positive interpretation of Tevelev degrees.

Contribution

It introduces a novel combinatorial approach using RSK to interpret Tevelev degrees, extending previous Schubert calculus methods.

Findings

RSK correspondence provides a positive combinatorial interpretation

New formulas relate algebraic geometry invariants to word combinatorics

Enhances understanding of curve enumeration in projective space

Abstract

The geometric Tevelev degrees of projective space enumerate general, pointed algebraic curves interpolating through the maximal possible number of points. Previous work expresses these invariants in terms of Schubert calculus. Extending ideas of Gillespie--Reimer-Berg, we use the RSK correspondence to give a positive interpretation of these counts in terms of the combinatorics of words.