Geodesic
Geometric aspects on Humbert-Edge curves of type 5, Kummer surfaces and hyperelliptic curves of genus 2
Glasgow mathematical journal, Tome 65 (2023) no. 3, pp. 612-624

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DOI

In this work, we study the Humbert-Edge curves of type 5, defined as a complete intersection of four diagonal quadrics in ${\mathbb{P}}^5$. We characterize them using Kummer surfaces, and using the geometry of these surfaces, we construct some vanishing thetanulls on such curves. In addition, we describe an argument to give an isomorphism between the moduli space of Humbert-Edge curves of type 5 and the moduli space of hyperelliptic curves of genus 2, and we show how this argument can be generalized to state an isomorphism between the moduli space of hyperelliptic curves of genus $g=\frac{n-1}{2}$ and the moduli space of Humbert-Edge curves of type $n\geq 5$ where $n$ is an odd number.
DOI : 10.1017/S0017089523000174
Mots-clés : Intersection of quadrics, Curves with automorphisms, Moduli spaces 
Castorena, Abel; Frías-Medina, Juan Bosco. Geometric aspects on Humbert-Edge curves of type 5, Kummer surfaces and hyperelliptic curves of genus 2. Glasgow mathematical journal, Tome 65 (2023) no. 3, pp. 612-624. doi: 10.1017/S0017089523000174
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     author = {Castorena, Abel and Fr{\'\i}as-Medina, Juan Bosco},
     title = {Geometric aspects on {Humbert-Edge} curves of type 5, {Kummer} surfaces and hyperelliptic curves of genus 2},
     journal = {Glasgow mathematical journal},
     pages = {612--624},
     year = {2023},
     volume = {65},
     number = {3},
     doi = {10.1017/S0017089523000174},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089523000174/}
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