Submission date: 1st October 2021

Abstract:

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.