Counting geometric branches via the Frobenius map and $F$-nilpotent singularities
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929531727642624 |
|---|---|
| author | Dao, Hailong Maddox, Kyle Pandey, Vaibhav |
| author_facet | Dao, Hailong Maddox, Kyle Pandey, Vaibhav |
| contents | We give an explicit formula to count the number of geometric branches of a curve in positive characteristic using the theory of tight closure. This formula readily shows that the property of having a single geometric branch characterizes $F$-nilpotent curves. Further, we show that a reduced, local $F$-nilpotent ring has a single geometric branch; in particular, it is a domain. Finally, we study inequalities of Frobenius test exponents along purely inseparable ring extensions with applications to $F$-nilpotent affine semigroup rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_16398 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Counting geometric branches via the Frobenius map and $F$-nilpotent singularities Dao, Hailong Maddox, Kyle Pandey, Vaibhav Commutative Algebra 13A35 (Primary) 13D45, 13B40 (Secondary) We give an explicit formula to count the number of geometric branches of a curve in positive characteristic using the theory of tight closure. This formula readily shows that the property of having a single geometric branch characterizes $F$-nilpotent curves. Further, we show that a reduced, local $F$-nilpotent ring has a single geometric branch; in particular, it is a domain. Finally, we study inequalities of Frobenius test exponents along purely inseparable ring extensions with applications to $F$-nilpotent affine semigroup rings. |
| title | Counting geometric branches via the Frobenius map and $F$-nilpotent singularities |
| topic | Commutative Algebra 13A35 (Primary) 13D45, 13B40 (Secondary) |
| url | https://arxiv.org/abs/2303.16398 |