Resolving the Singularities of Splitting Loci

2025/07/01 by Lin, Feiyang · 2 citations
#14D20 #14H51 #14M12 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.01233

Abstract

We construct modular resolutions of singularities for splitting loci, and use them to show that tame splitting loci have rational singularities. As a corollary of our results and Hurwitz-Brill-Noether theory, we prove that if C is a general k-gonal curve, the components of W^r_d(C) have rational singularities. We also recover the classical Gieseker-Petri theorem. Along the way, we prove a cohomology vanishing statement for certain tautological vector bundles on Quot^r,d_ℙ¹(O^{⊕ N}), which may be of independent interest.

Citations

• Quantum K‐invariants via Quot schemes II
• A picture of the irreducible components of W^r_d(C) for a general k-gonal curve C
• On the cohomology of tautological bundles over Quot schemes of curves
• Euler characteristics of tautological bundles over Quot schemes of curves
• A refined Brill–Noether theory over Hurwitz spaces
• Relative Beilinson Monad and Direct Image for Families of Coherent Sheaves
• Hankel determinantal rings have rational singularities

Cited by

• The locally free locus of Quot schemes on ℙ¹
• A Borel--Weil--Bott theorem for Quot schemes on ℙ¹

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