Variety of singular quadrics containing a projective curve
Annales de l'Institut Fourier, Volume 69 (2019) no. 4, p. 1879-1896

We study the variety of quadrics of rank at most k in 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+r1. By considering the loci where this expectation is not true, we construct new divisor classes in ¯ g,n . We use one of these classes to show that ¯ 15,9 is of general type.

Nous étudions la variété de quadriques de rang au maximum k en 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+r1. En considérant le lieu où la dimension est différente, nous construisons des nouvelles classes de diviseurs dans ¯ g,n . Nous utilisons une de ces classes pour montrer que ¯ 15,9 est de type général.

Received : 2017-07-24
Revised : 2018-03-21
Accepted : 2018-06-13
Published online : 2019-09-16
DOI : https://doi.org/10.5802/aif.3284
Classification:  14H10,  14H51
Keywords: moduli space, singular quadrics
@article{AIF_2019__69_4_1879_0,
     author = {Kadik\"oyl\"u, \.Irfan},
     title = {Variety of singular quadrics containing a projective curve},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {69},
     number = {4},
     year = {2019},
     pages = {1879-1896},
     doi = {10.5802/aif.3284},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2019__69_4_1879_0}
}
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/item/AIF_2019__69_4_1879_0/

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