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Funktsional. Anal. i Prilozhen., 2015, Volume 49, Issue 1, Pages 49–61 (Mi faa3183)  

Systems of Polynomial Equations Defining Hyperelliptic $d$-Osculating Covers

A. Treibichab

a Universit'e d'Artois, Laboratoire de Math'ematique de Lens
b Universidad de la República del Uruguay, Regional Norte

Abstract: Let $X$ denote a fixed smooth projective curve of genus $1$ defined over an algebraically closed field $\mathbb{K}$ of arbitrary characteristic $\boldsymbol{p}\neq2$. 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 $d>1$.

Keywords: finite separable covers, hyperelliptic curves, Weierstrass points

DOI: https://doi.org/10.4213/faa3183

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English version:
Functional Analysis and Its Applications, 2015, 49:1, 40–49

Bibliographic databases:

UDC: 517.9
Received: 26.10.2012

Citation: A. Treibich, “Systems of Polynomial Equations Defining Hyperelliptic $d$-Osculating Covers”, Funktsional. Anal. i Prilozhen., 49:1 (2015), 49–61; Funct. Anal. Appl., 49:1 (2015), 40–49

Citation in format AMSBIB
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\pages 49--61
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  • https://doi.org/10.4213/faa3183
  • http://mi.mathnet.ru/eng/faa/v49/i1/p49

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