Degree of Unirationality for del Pezzo Surfaces over Finite Fields
Journal de Théorie des Nombres de Bordeaux, Tome 27 (2015) no. 1, pp. 171-182.

Nous abordons la question du degré de paramétrisation unirationnelle de surfaces de del Pezzo de degré quatre et trois. Plus précisément, nous montrons que les surfaces de del Pezzo de degré quatre sur les corps finis admettent des paramétrisations de degré deux, et que les surfaces cubiques minimales admettent des paramétrisations de degré six. Il reste incertain s’il existe des paramétrisations de degré trois ou quatre pour ces dernières surfaces.

We address the question of the degree of unirational parameterizations of degree four and degree three del Pezzo surfaces. Specifically we show that degree four del Pezzo surfaces over finite fields admit degree two parameterizations and minimal cubic surfaces admit parameterizations of degree six. It is an open question whether or not minimal cubic surfaces over finite fields can admit degree three or four parameterizations.

Reçu le : 2013-07-09
Révisé le : 2014-07-06
Accepté le : 2014-07-09
Publié le : 2015-05-21
DOI : https://doi.org/10.5802/jtnb.897
Classification : 14J26
@article{JTNB_2015__27_1_171_0,
     author = {Amanda Knecht},
     title = {Degree of Unirationality for del Pezzo Surfaces over Finite Fields},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {27},
     number = {1},
     year = {2015},
     pages = {171-182},
     doi = {10.5802/jtnb.897},
     mrnumber = {3346968},
     language = {en},
     url = {jtnb.centre-mersenne.org/item/JTNB_2015__27_1_171_0/}
}
Amanda Knecht. Degree of Unirationality for del Pezzo Surfaces over Finite Fields. Journal de Théorie des Nombres de Bordeaux, Tome 27 (2015) no. 1, pp. 171-182. doi : 10.5802/jtnb.897. https://jtnb.centre-mersenne.org/item/JTNB_2015__27_1_171_0/

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