Symmetric power of higher dimensional varieties

Ashima Bansal; Supravat Sarkar; Shivam Vats

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arXiv · 2508.12654

Symmetric power of higher dimensional varieties

Ashima Bansal·Supravat Sarkar·Shivam Vats

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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.

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Ashima Bansal, Supravat Sarkar, Shivam Vats. 2025-08-18. Symmetric power of higher dimensional varieties. https://arxiv.org/abs/2508.12654

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