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arXiv · 2006.06603

Logarithmic Donaldson-Thomas theory

Davesh Maulik·Dhruv Ranganathan
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Abstract

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.

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Davesh Maulik, Dhruv Ranganathan. 2020-06-11. Logarithmic Donaldson-Thomas theory. https://arxiv.org/abs/2006.06603

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