Haupt's theorem for strata of abelian differentials
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2020
- DOI:
- 10.48550/arXiv.2002.12901
- arXiv:
- arXiv:2002.12901
- Bibcode:
- 2020arXiv200212901B
- Keywords:
-
- Mathematics - Geometric Topology;
- Mathematics - Algebraic Geometry;
- Mathematics - Complex Variables;
- 30F30;
- 30F60;
- 57M10;
- 14H55