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Logarithmic Donaldson-Thomas theory

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Maulik, D 
Ranganathan, D 

Abstract

jats:titleAbstract</jats:title> jats:pLet X be a smooth and projective threefold with a simple normal crossings divisor D. We construct the Donaldson–Thomas theory of the pair jats:inline-formula jats:alternatives <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S2050508624000015_inline1.png" /> jats:tex-math (X|D) </jats:tex-math> </jats:alternatives> </jats:inline-formula> 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.</jats:p>

Description

Keywords

4902 Mathematical Physics, 4904 Pure Mathematics, 49 Mathematical Sciences

Journal Title

Forum of Mathematics, Pi

Conference Name

Journal ISSN

2050-5086
2050-5086

Volume Title

Publisher

Cambridge University Press (CUP)
Sponsorship
EPSRC (EP/V051830/1)