Abstract
Let S be a closed topological surface. Haupt’s theorem provides necessary and sufficient conditions for a complex-valued character of the first integer homology group of S to be realized by integration against a complex-valued 1-form that is holomorphic with respect to some complex structure on S. We prove a refinement of this theorem that takes into account the divisor data of the 1-form.
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This work was supported by a grant from the Simons Foundation (713192, MB).
This work was supported by a grant from the Simons Foundation (585547, CJu).
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Bainbridge, M., Johnson, C., Judge, C. et al. Haupt’s theorem for strata of abelian differentials. Isr. J. Math. 252, 429–459 (2022). https://doi.org/10.1007/s11856-022-2381-8
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DOI: https://doi.org/10.1007/s11856-022-2381-8