Bulletin of the Korean Mathematical Society (대한수학회보)

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MINIMAL DEL PEZZO SURFACES OF DEGREE 2 OVER FINITE FIELDS

  • Received : 2016.09.19
  • Accepted : 2016.12.26
  • Published : 2017.09.30
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Abstract

Let X be a minimal del Pezzo surface of degree 2 over a finite field ${\mathbb{F}}_q$. The image ${\Gamma}$ of the Galois group Gal(${\bar{\mathbb{F}}}_q/{\mathbb{F}}_q$) in the group Aut($Pic({\bar{X}})$) is a cyclic subgroup of the Weyl group W($E_7$). There are 60 conjugacy classes of cyclic subgroups in W($E_7$) and 18 of them correspond to minimal del Pezzo surfaces. In this paper we study which possibilities of these subgroups for minimal del Pezzo surfaces of degree 2 can be achieved for given q.

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Acknowledgement

Supported by : Russian Foundation for Sciences

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