Tokyo Journal of Mathematics

Characterization of Non-F-split del Pezzo Surfaces of Degree 2

Natsuo SAITO

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Abstract

We investigate a smooth del Pezzo surface of degree 2 which is not Frobenius split. We give a characterization of non-F-split del Pezzo surfaces of degree 2 which exist only if the characteristic of the ground field is 2 or 3. Moreover, we prove that the set of centers of the blow-ups on $\mathbb{P}^{2}$ which gives a non-F-split del Pezzo surface is projectively equivalent to the only complete 7-arc over $\mathbb{F}_{9}$ if the characteristic is 3.

Article information

Source
Tokyo J. Math., Volume 40, Number 1 (2017), 247-253.

Dates
First available in Project Euclid: 8 August 2017

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1502179226

Digital Object Identifier
doi:10.3836/tjm/1502179226

Mathematical Reviews number (MathSciNet)
MR3689989

Zentralblatt MATH identifier
06787098

Subjects
Primary: 14J26: Rational and ruled surfaces

Citation

SAITO, Natsuo. Characterization of Non-F-split del Pezzo Surfaces of Degree 2. Tokyo J. Math. 40 (2017), no. 1, 247--253. doi:10.3836/tjm/1502179226. https://projecteuclid.org/euclid.tjm/1502179226


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