2025/10/30 by Lin, Feiyang
#14B05 #14D20 #14M12 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2510.26044
Splitting loci are certain natural closed substacks of the stack of vector bundles on ℙ1, which have found interesting applications in the Brill-Noether theory of k-gonal curves. In this paper, we completely characterize when splitting loci, as algebraic stacks, are Gorenstein or ℚ-Gorenstein. The main ingredients of the proof are a computation of the class groups of splitting loci in certain affine extension spaces, and a formula for the class of their canonical module.