Symmetric power of higher dimensional varieties

2025/08/18 by Bansal, Ashima, Sarkar, Supravat, Vats, Shivam · 2 citations
#14B05 #14J17 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.12654

Abstract

We study several properties of the symmetric power S^mX of a smooth variety X. We describe the Picard and divisor class groups of S^mX when X is projective. We give a complete description of the stratification of S^mX by iterated singular locus in terms of some combinatorial data regarding partitions of the integer m. This gives a new viewpoint of a natural stratification of S^mX by multiplicities.

Citations

• Automorphisms of Hilbert Schemes of Points on Abelian Surfaces
• Automorphisms of symmetric powers and motivic zeta functions
• Fano Varieties with Large Degree Endomorphisms
• Symmetric products of surfaces; a unifying theme for topology and physics
• Questions on self maps of algebraic varieties
• The McKay correspondence for finite subgroups of SL(3,\C)

Cited by

• Isomorphisms and automorphisms of multiprojective bundles and symmetric powers of projective bundles
• Automorphisms of punctual Hilbert schemes and symmetric powers of varieties

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