Curves in projective space and RSK

2025/08/27 by Lian, Carl, Solotko, Saskia
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.19503

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.

Citations

• Enumerating log rational curves on some toric varieties
• Curves on Hirzebruch Surfaces and Semistability
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• Virtual intersections on the Quot-scheme and Vafa-Intriligator formulas
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Related

• Asymptotic geometric Tevelev degrees of hypersurfaces
• A Generalized RSK for Enumerating Linear Series on n-pointed Curves
• Counting curves on surfaces: a guide to new techniques and results
• Generalized Tevelev degrees of ℙ¹
• Curve neighborhoods of Schubert varieties