Nonclassical Godeaux surfaces in characteristic five
Abstract: A classical Godeaux surface is a smooth minimal projective surface , with , and . A nonclassical Godeaux surface is a smooth minimal projective surface with , , and or ; such surfaces should exist in characteristic 5. It is the purpose of this note to construct nonclassical Godeaux surfaces in characteristic 5, with . The method is to exhibit a smooth quintic surface on which acts, so that the quotient is smooth; this quotient is the desired surface.
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