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arXiv · 2309.02684

Functions on the moduli space of projective structures on complex curves

Indranil Biswas
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Abstract

We investigate the moduli space ${\mathcal P}_g$ of smooth complex projective curves of genus $g$ equipped with a projective structure. When $g\, \geq\, 3$, it is shown that this moduli space ${\mathcal P}_g$ does not admit any nonconstant algebraic function. This is in contrast with the case of ${\mathcal P}_2$ which is known to be an affine variety.

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Indranil Biswas. 2023-09-06. Functions on the moduli space of projective structures on complex curves. https://arxiv.org/abs/2309.02684

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