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Preprint Number 2069

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2069. Darío García, Pedro Rizzo, Joel Torres del Valle
A note on the definability of genus for Zariski geometries

Submission date: 1st October 2021


In this work we propose a notion of genus in the context of Zariski geometries and we obtain natural generalizations of the Riemann Hurwitz Theorem and the Hurwitz Theorem in the context of very ample Zariski geometries. As a corollary, we show that such notion of genus cannot be first-order definable in the full language of a Zariski geometry.

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Full text arXiv 2110.02218: pdf, ps.

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