Symmetric power of higher dimensional varieties
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911109742592000 |
|---|---|
| author | Bansal, Ashima Sarkar, Supravat Vats, Shivam |
| author_facet | Bansal, Ashima Sarkar, Supravat Vats, Shivam |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12654 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symmetric power of higher dimensional varieties Bansal, Ashima Sarkar, Supravat Vats, Shivam Algebraic Geometry 14B05, 14J17 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. |
| title | Symmetric power of higher dimensional varieties |
| topic | Algebraic Geometry 14B05, 14J17 |
| url | https://arxiv.org/abs/2508.12654 |