Abstract
Let X denote a fixed smooth projective curve of genus 1 defined over an algebraically closed field \(\mathbb{K}\) of arbitrary characteristic p ≠ 2. For any positive integer n, we consider the moduli space H(X, n) of degree-n finite separable covers of X by a hyperelliptic curve with three marked Weierstrass points. We parameterize H(X, n) by a suitable space of rational fractions and apply it to studying the (finite) subset of degree-n hyperelliptic tangential covers of X. We find a polynomial characterization for the corresponding rational fractions and deduce a square system of polynomial equations whose solutions parameterize these covers. Furthermore, we also obtain nonsquare systems parameterizing hyperelliptic d-osculating covers for any d > 1.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 49, No. 1, pp. 49–61, 2015
Original Russian Text Copyright © by Armando Treibich
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Treibich, A. Systems of polynomial equations defining hyperelliptic d-osculating covers. Funct Anal Its Appl 49, 40–49 (2015). https://doi.org/10.1007/s10688-015-0081-4
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DOI: https://doi.org/10.1007/s10688-015-0081-4