no. 4
Variety of singular quadrics containing a projective curve
Kadiköylü, İrfan1
1 Humboldt-Universität zu Berlin Institut für Mathematik 10099 Berlin (Germany)
Annales de l'Institut Fourier, Volume 69 (2019) no. 4, pp. 1879-1896.

We study the variety of quadrics of rank at most k in ℙ r , containing a general projective curve of genus g and degree d and show that it has the expected dimension in the range g-d+r≤1. By considering the loci where this expectation is not true, we construct new divisor classes in ℳ ¯ g,n . We use one of these classes to show that ℳ ¯ 15,9 is of general type.

Nous étudions la variété de quadriques de rang au maximum k en ℙ r contenant une courbe projective générale de genre g et de degré d et nous montrons qu’elle a la dimension attendue dans le cas g-d+r≤1. En considérant le lieu où la dimension est différente, nous construisons des nouvelles classes de diviseurs dans ℳ ¯ g,n . Nous utilisons une de ces classes pour montrer que ℳ ¯ 15,9 est de type général.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/aif.3284
Classification: 14H10, 14H51
Keywords: moduli space, singular quadrics
Mots-clés : espace de modules, quadriques singulières

Kadiköylü, İrfan 1

1 Humboldt-Universität zu Berlin Institut für Mathematik 10099 Berlin (Germany)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Kadiköylü, İrfan. Variety of singular quadrics containing a projective curve. Annales de l'Institut Fourier, Volume 69 (2019) no. 4, pp. 1879-1896. doi : 10.5802/aif.3284. https://aif.centre-mersenne.org/articles/10.5802/aif.3284/

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