Triangulated characterizations of singularities
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912258204893184 |
|---|---|
| author | Lank, Pat Venkatesh, Sridhar |
| author_facet | Lank, Pat Venkatesh, Sridhar |
| contents | This work presents a range of triangulated characterizations for important classes of singularities such as derived splinters, rational singularities, and Du Bois singularities. An invariant called 'level' in a triangulated category can be used to measure the failure of a variety to have a prescribed singularity type. We provide explicit computations of this invariant for reduced Nagata schemes of Krull dimension one and for affine cones over smooth projective hypersurfaces. Furthermore, these computations are utilized to produce upper bounds for Rouquier dimension on the respective bounded derived categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04389 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Triangulated characterizations of singularities Lank, Pat Venkatesh, Sridhar Algebraic Geometry Commutative Algebra 14F08 (primary), 14B05 (secondary), 14F17, 14A30, 14E15, 18G80 This work presents a range of triangulated characterizations for important classes of singularities such as derived splinters, rational singularities, and Du Bois singularities. An invariant called 'level' in a triangulated category can be used to measure the failure of a variety to have a prescribed singularity type. We provide explicit computations of this invariant for reduced Nagata schemes of Krull dimension one and for affine cones over smooth projective hypersurfaces. Furthermore, these computations are utilized to produce upper bounds for Rouquier dimension on the respective bounded derived categories. |
| title | Triangulated characterizations of singularities |
| topic | Algebraic Geometry Commutative Algebra 14F08 (primary), 14B05 (secondary), 14F17, 14A30, 14E15, 18G80 |
| url | https://arxiv.org/abs/2405.04389 |