Abstract
In this paper, we focus on relations between holomorphic 1-forms and holomorphic 1-cochains on a closed Riemann surface. Holomorphic 1-cochains are defined by Wilson in 2008 using a combinatorial Hodge theory. A holomorphic 1-form is characterized by its periods. So is a holomorphic 1-cochain. We consider relations between a holomorphic 1-form and a holomorphic 1-cochain which have the same periods and show that holomorphic 1-cochains provide an approximation of holomorphic 1-forms.
Citation
Daisuke Yamaki. "The asymptotic behavior of holomorphic 1-cochains." Kodai Math. J. 39 (2) 297 - 317, June 2016. https://doi.org/10.2996/kmj/1467830139
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