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arXiv · 1304.6798

On the Unirationality of del Pezzo surfaces of degree two

Cecília Salgado·Damiano Testa·Anthony Várilly-Alvarado
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Abstract

Among geometrically rational surfaces, del Pezzo surfaces of degree two over a field k containing at least one point are arguably the simplest that are not known to be unirational over k. Looking for k-rational curves on these surfaces, we extend some earlier work of Manin on this subject. We then focus on the case where k is a finite field, where we show that all except possibly three explicit del Pezzo surfaces of degree two are unirational over k.

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Cecília Salgado, Damiano Testa, Anthony Várilly-Alvarado. 2013-04-25. On the Unirationality of del Pezzo surfaces of degree two. https://doi.org/10.1112/jlms%2Fjdu014

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