Geodesic
ON THE MONODROMY AND GALOIS GROUP OF CONICS LYING ON HEISENBERG INVARIANT QUARTIC K3 SURFACES
Glasgow mathematical journal, Tome 62 (2020) no. 3, pp. 640-660

Voir la notice de l'article provenant de la source Cambridge University Press

In [5], Eklund showed that a general (Z/2Z)4 -invariant quartic K3 surface contains at least 320 conics. In this paper, we analyse the field of definition of those conics as well as their Monodromy group. As a result, we prove that the moduli space of (Z/2Z)4-invariant quartic K3 surface with a certain marked conic has 10 irreducible components. 
BOUYER, FLORIAN. ON THE MONODROMY AND GALOIS GROUP OF CONICS LYING ON HEISENBERG INVARIANT QUARTIC K3 SURFACES. Glasgow mathematical journal, Tome 62 (2020) no. 3, pp. 640-660. doi: 10.1017/S0017089519000399
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[1] Barth, W. and Nieto, I., Abelian surfaces of type (1,3) and quartic surfaces with 16 skew lines, J. Algebraic Geom. 3(2) (1994), 173–222. MR 1257320 Google Scholar

[2] Bosma, W., Cannon, J. and Playoust, C., The Magma algebra system. I. The user language, J. Symbolic Comput. 24(3–4) (1997), 235–265, Computational algebra and number theory (London, 1993). MR MR1484478 Google Scholar | DOI

[3] Bouyer, F., Magma Code. Available at https://sites.google.com/site/fjscbouyer/publication/magma-code. Google Scholar

[4] Ciliberto, C. and Dedieu, T., On universal Severi varieties of low genus surfaces, Math. Z. 271(3–4) (2012), 953–960. MR 2945592 Google Scholar | DOI

[5] Eklund, D., Curves on Heisenberg invariant quartic surfaces in projective 3-space, Eur. J. Math. 4(3) (2018), 931–952. Google Scholar | DOI

[6] Kemeny, M., The universal Severi variety of rational curves on K3 surfaces, Bull. Lond. Math. Soc. 45(1) (2013), 159–174. MR 3033964 Google Scholar | DOI

[7] Mumford, D., On the equations defining abelian varieties. I, Invent. Math. 1 (1966), 287–354. MR 0204427 Google Scholar | DOI

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