Integral Models of Extremal Rational Elliptic Surfaces

Details Integral Models of Extremal Rational Elliptic Surfaces Integral Models of Extremal Rational Elliptic Surfaces

2009-08-13

arxiv.org/abs/0908.1831v2

Mathematics

Algebraic Geometry

15 pages, minor revision. To appear in Communications in Algebra

Scientific paper

Miranda and Persson classified all extremal rational elliptic surfaces in characteristic zero. We show that each surface in Miranda and Persson's classification has an integral model with good reduction everywhere (except for those of type X_{11}(j), which is an exceptional case), and that every extremal rational elliptic surface over an algebraically closed field of characteristic p > 0 can be obtained by reducing one of these integral models mod p.

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