Note on Euler characteristic of a toric vector bundle
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910106717782016 |
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| author | Chong, Suhyon Huang, Shaoyu Kaveh, Kiumars |
| author_facet | Chong, Suhyon Huang, Shaoyu Kaveh, Kiumars |
| contents | A convex chain is a finite integer linear combination of indicator functions of convex polytopes. Khovanskii-Pukhlikov extend the Ehrhart theory of convex lattice polytopes to the setting of convex chains. Extending the relationship between equivariant line bundles on projective toric varieties and virtual lattice polytopes, we associate a lattice convex chain to a torus equivariant vector bundle on a toric variety and show that sum of values of this convex chain on lattice points gives the Euler characteristic of the bundle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_22514 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Note on Euler characteristic of a toric vector bundle Chong, Suhyon Huang, Shaoyu Kaveh, Kiumars Algebraic Geometry 14M25 (Primary), 14J60 (Secondary) A convex chain is a finite integer linear combination of indicator functions of convex polytopes. Khovanskii-Pukhlikov extend the Ehrhart theory of convex lattice polytopes to the setting of convex chains. Extending the relationship between equivariant line bundles on projective toric varieties and virtual lattice polytopes, we associate a lattice convex chain to a torus equivariant vector bundle on a toric variety and show that sum of values of this convex chain on lattice points gives the Euler characteristic of the bundle. |
| title | Note on Euler characteristic of a toric vector bundle |
| topic | Algebraic Geometry 14M25 (Primary), 14J60 (Secondary) |
| url | https://arxiv.org/abs/2601.22514 |