Counting sheaves on Calabi-Yau 4-folds, I
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866913942828220416 |
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| author | Oh, Jeongseok Thomas, Richard P. |
| author_facet | Oh, Jeongseok Thomas, Richard P. |
| contents | Borisov-Joyce constructed a real virtual cycle on compact moduli spaces of stable sheaves on Calabi-Yau 4-folds, using derived differential geometry.
We construct an algebraic virtual cycle. A key step is a localisation of Edidin-Graham's square root Euler class for $SO(r,\mathbb C)$ bundles to the zero locus of an isotropic section, or to the support of an isotropic cone.
We prove a torus localisation formula, making the invariants computable and extending them to the noncompact case when the fixed locus is compact.
We give a $K$-theoretic refinement by defining $K$-theoretic square root Euler classes and their localised versions.
In a sequel we prove our invariants reproduce those of Borisov-Joyce. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_05542 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Counting sheaves on Calabi-Yau 4-folds, I Oh, Jeongseok Thomas, Richard P. Algebraic Geometry High Energy Physics - Theory 14N35, 14C17 Borisov-Joyce constructed a real virtual cycle on compact moduli spaces of stable sheaves on Calabi-Yau 4-folds, using derived differential geometry. We construct an algebraic virtual cycle. A key step is a localisation of Edidin-Graham's square root Euler class for $SO(r,\mathbb C)$ bundles to the zero locus of an isotropic section, or to the support of an isotropic cone. We prove a torus localisation formula, making the invariants computable and extending them to the noncompact case when the fixed locus is compact. We give a $K$-theoretic refinement by defining $K$-theoretic square root Euler classes and their localised versions. In a sequel we prove our invariants reproduce those of Borisov-Joyce. |
| title | Counting sheaves on Calabi-Yau 4-folds, I |
| topic | Algebraic Geometry High Energy Physics - Theory 14N35, 14C17 |
| url | https://arxiv.org/abs/2009.05542 |