Vanishing theorems for combinatorial geometries
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_ | 1866916992852688896 |
|---|---|
| author | Eur, Christopher Fink, Alex Larson, Matt |
| author_facet | Eur, Christopher Fink, Alex Larson, Matt |
| contents | We establish strong vanishing theorems for line bundles on wonderful varieties of hyperplane arrangements, and we show that the resulting positivity properties of Euler characteristics extend to all matroids. We achieve this by showing that every degeneration of a wonderful variety within the permutohedral toric variety is reduced and Cohen--Macaulay. The same holds for a larger class of subschemes in products of projective lines that we call "kindred," which are characterized by matroidal Hilbert polynomials. Our results give a new proof of the 20-year-old f-vector conjecture of Speyer and resolve the conjecture of Tohaneanu that higher order Orlik--Terao algebras are Cohen--Macaulay. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05207 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Vanishing theorems for combinatorial geometries Eur, Christopher Fink, Alex Larson, Matt Algebraic Geometry Commutative Algebra Combinatorics We establish strong vanishing theorems for line bundles on wonderful varieties of hyperplane arrangements, and we show that the resulting positivity properties of Euler characteristics extend to all matroids. We achieve this by showing that every degeneration of a wonderful variety within the permutohedral toric variety is reduced and Cohen--Macaulay. The same holds for a larger class of subschemes in products of projective lines that we call "kindred," which are characterized by matroidal Hilbert polynomials. Our results give a new proof of the 20-year-old f-vector conjecture of Speyer and resolve the conjecture of Tohaneanu that higher order Orlik--Terao algebras are Cohen--Macaulay. |
| title | Vanishing theorems for combinatorial geometries |
| topic | Algebraic Geometry Commutative Algebra Combinatorics |
| url | https://arxiv.org/abs/2510.05207 |