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- W4300229679 abstract "We show that a large class of maximally degenerating families of n-dimensional polarized varieties come with a canonical basis of sections of powers of the ample line bundle. The families considered are obtained by smoothing a reducible union of toric varieties governed by a wall structure on a real n-(pseudo-)manifold. Wall structures have previously been constructed inductively for cases with locally rigid singularities and by Gromov-Witten theory for mirrors of log Calabi-Yau surfaces and K3 surfaces by various combinations of the authors. For trivial wall structures on the n-torus we retrieve the classical theta functions. Possible applications include mirror symmetry, geometric compactifications of moduli of certain polarized varieties via stable pairs and geometric quantization." @default.
- W4300229679 created "2022-10-03" @default.
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- W4300229679 date "2016-01-26" @default.
- W4300229679 modified "2023-10-17" @default.
- W4300229679 title "Theta functions on varieties with effective anti-canonical class" @default.
- W4300229679 doi "https://doi.org/10.48550/arxiv.1601.07081" @default.
- W4300229679 hasPublicationYear "2016" @default.
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