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Let $X$ be a minimal del Pezzo surface of degree $2$ over a finite field $\F_q$. The image $\Gamma$ of the Galois group $\Gal(\overline{\F}_q / \F_q)$ in the group $\Aut(\Pic(\XX))$ 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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참고문헌 (10)
참고문헌 신청
B. Banwait / Del Pezzo surfaces over finite fields and their Frobenius traces
R. W. Carter / 1972 / Conjugacy classes in the weyl group / Compositio Math 25:1~59
V. A. Iskovskikh / 1979 / Minimal models of rational surfaces over arbitrary field / Math. USSR Izv 43:19~43
V. A. Iskovskikh / 1996 / Factorization of birational mappings of rational surfaces from the point of view of Mori theory / Russian Math. Surveys 51:585~652
Yu. I. Manin / 1974 / North-Holland Mathe-matical Library, Vol. 4 / North-Holland Publishing Co., American Elsevier Publishing Co.
R. W. Carter / 1972 / Conjugacy classes in the weyl group / Compositio Math 25:1~59
V. A. Iskovskikh / 1979 / Minimal models of rational surfaces over arbitrary field / Math. USSR Izv 43:19~43
V. A. Iskovskikh / 1996 / Factorization of birational mappings of rational surfaces from the point of view of Mori theory / Russian Math. Surveys 51:585~652
Yu. I. Manin / 1974 / North-Holland Mathe-matical Library, Vol. 4 / North-Holland Publishing Co., American Elsevier Publishing Co.
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