Verlinde formulae on complex surfaces: K-theoretic invariants
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2019
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| _version_ | 1866910905761005568 |
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| author | Göttsche, L. Kool, M. Williams, R. A. |
| author_facet | Göttsche, L. Kool, M. Williams, R. A. |
| contents | We conjecture a Verlinde type formula for the moduli space of Higgs sheaves on a surface with a holomorphic 2-form. The conjecture specializes to a Verlinde formula for the moduli space of sheaves. Our formula interpolates between $K$-theoretic Donaldson invariants studied by the first named author and Nakajima-Yoshioka and $K$-theoretic Vafa-Witten invariants introduced by Thomas and also studied by the first and second named authors. We verify our conjectures in many examples (e.g. on K3 surfaces). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1903_03869 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Verlinde formulae on complex surfaces: K-theoretic invariants Göttsche, L. Kool, M. Williams, R. A. Algebraic Geometry High Energy Physics - Theory Differential Geometry 14D20, 14D21, 14J60, 14J80, 14J81 We conjecture a Verlinde type formula for the moduli space of Higgs sheaves on a surface with a holomorphic 2-form. The conjecture specializes to a Verlinde formula for the moduli space of sheaves. Our formula interpolates between $K$-theoretic Donaldson invariants studied by the first named author and Nakajima-Yoshioka and $K$-theoretic Vafa-Witten invariants introduced by Thomas and also studied by the first and second named authors. We verify our conjectures in many examples (e.g. on K3 surfaces). |
| title | Verlinde formulae on complex surfaces: K-theoretic invariants |
| topic | Algebraic Geometry High Energy Physics - Theory Differential Geometry 14D20, 14D21, 14J60, 14J80, 14J81 |
| url | https://arxiv.org/abs/1903.03869 |