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Theta functions, broken lines and 2-marked log Gromov-Witten invariants

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arxiv 2204.12257 v1 pith:RIWFX3IW submitted 2022-04-26 math.AG

Tim Graefnitz This is my paper · ORCID
classification math.AG
keywords gromov-witteninvariantsfunctionsmarkedthetaanticanonicalcertaindivisor
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Theta functions were defined for varieties with effective anticanonical divisor and are related to certain punctured Gromov-Witten invariants. In this paper we show that in the case of a log Calabi-Yau surface (X,D) with smooth very ample anticanonical divisor we can circumvent the notion of punctured Gromov-Witten invariants and relate theta functions and their multiplicative structure to certain 2-marked log Gromov-Witten invariants. This is a natural extension of the correspondence between wall functions and 1-marked log Gromov-Witten invariants.

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  1. Quantum periods, toric degenerations and intrinsic mirror symmetry

    math.AG 2025-01 conditional novelty 7.0 of 10

    The classical periods of the intrinsic mirror algebra of a log Calabi-Yau Fano pair reproduce the regularized quantum periods of the Fano variety.

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