Toric sheaves and flips
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914956413239296 |
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| author | Clarke, Andrew Napame, Achim Tipler, Carl |
| author_facet | Clarke, Andrew Napame, Achim Tipler, Carl |
| contents | Any toric flip naturally induces an equivalence between the associated categories of equivariant reflexive sheaves, and we investigate how slope stability behaves through this functor. On one hand, for a fixed toric sheaf, and natural polarisations that make the exceptional loci small, we provide a simple numerical criterion that characterizes when slope stability is preserved through the flip. On the other hand, for a given flip, we introduce full subcategories of logarithmic toric sheaves and characterize when polystability is preserved for all toric sheaves in those subcategories at once. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09267 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Toric sheaves and flips Clarke, Andrew Napame, Achim Tipler, Carl Algebraic Geometry 14M25 Any toric flip naturally induces an equivalence between the associated categories of equivariant reflexive sheaves, and we investigate how slope stability behaves through this functor. On one hand, for a fixed toric sheaf, and natural polarisations that make the exceptional loci small, we provide a simple numerical criterion that characterizes when slope stability is preserved through the flip. On the other hand, for a given flip, we introduce full subcategories of logarithmic toric sheaves and characterize when polystability is preserved for all toric sheaves in those subcategories at once. |
| title | Toric sheaves and flips |
| topic | Algebraic Geometry 14M25 |
| url | https://arxiv.org/abs/2309.09267 |