Logarithmic Donaldson-Thomas theory
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866913186098184192 |
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| author | Maulik, Davesh Ranganathan, Dhruv |
| author_facet | Maulik, Davesh Ranganathan, Dhruv |
| contents | Let $X$ be a smooth threefold with a simple normal crossings divisor $D$. We construct the Donaldson-Thomas theory of the pair $(X|D)$ enumerating ideal sheaves on $X$ relative to $D$. These moduli spaces are compactified by studying subschemes in expansions of the target geometry, and the moduli space carries a virtual fundamental class leading to numerical invariants with expected properties. We formulate punctual evaluation, rationality and wall-crossing conjectures, in parallel with the standard theory. Our formalism specializes to the Li-Wu theory of relative ideal sheaves when the divisor is smooth, and is parallel to recent work on logarithmic Gromov-Witten theory with expansions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2006_06603 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Logarithmic Donaldson-Thomas theory Maulik, Davesh Ranganathan, Dhruv Algebraic Geometry 14N35, 14A21, 14T90 Let $X$ be a smooth threefold with a simple normal crossings divisor $D$. We construct the Donaldson-Thomas theory of the pair $(X|D)$ enumerating ideal sheaves on $X$ relative to $D$. These moduli spaces are compactified by studying subschemes in expansions of the target geometry, and the moduli space carries a virtual fundamental class leading to numerical invariants with expected properties. We formulate punctual evaluation, rationality and wall-crossing conjectures, in parallel with the standard theory. Our formalism specializes to the Li-Wu theory of relative ideal sheaves when the divisor is smooth, and is parallel to recent work on logarithmic Gromov-Witten theory with expansions. |
| title | Logarithmic Donaldson-Thomas theory |
| topic | Algebraic Geometry 14N35, 14A21, 14T90 |
| url | https://arxiv.org/abs/2006.06603 |