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arXiv · 1603.01877

Algebraic dimension of complex nilmanifolds

Anna Fino·Gueo Grantcharov·Misha Verbitsky
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Abstract

Let M be a complex nilmanifold, that is, a compact quotient of a nilpotent Lie group endowed with an invariant complex structure by a discrete lattice. A holomorphic differential on M is a closed, holomorphic 1-form. We show that $a(M)\leq k$, where $a(M)$ is the algebraic dimension $a(M)$ (i.e. the transcendence degree of the field of meromorphic functions) and $k$ is the dimension of the space of holomorphic differentials. We prove a similar result about meromorphic maps to Kahler manifolds.

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Anna Fino, Gueo Grantcharov, Misha Verbitsky. 2016-03-06. Algebraic dimension of complex nilmanifolds. https://doi.org/10.1016/j.matpur.2017.11.010

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