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On a stratification of the moduli of K3 surfaces

Gerard van der Geer, T. Katsura (2000)

Journal of the European Mathematical Society

In this paper we give a characterization of the height of K3 surfaces in characteristic p > 0 . This enables us to calculate the cycle classes in families of K3 surfaces of the loci where the height is at least h . The formulas for such loci can be seen as generalizations of the famous formula of Deuring for the number of supersingular elliptic curves in characteristic p . In order to describe the tangent spaces to these loci we study the first cohomology of higher closed forms.

On a theorem of Tate

Fedor Bogomolov, Yuri Tschinkel (2008)

Open Mathematics

We study applications of divisibility properties of recurrence sequences to Tate’s theory of abelian varieties over finite fields.

On the automorphisms of surfaces of general type in positive characteristic

Edoardo Ballico (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Here we give an explicit polynomial bound (in term of K X 2 and not depending on the prime p ) for the order of the automorphism group of a minimal surface X of general type defined over a field of characteristic p > 0 .

On the automorphisms of surfaces of general type in positive characteristic, II

Edoardo Ballico (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Here we give an upper polynomial bound (as function of K X 2 but independent on p ) for the order of a p -subgroup of A u t X r e d with X minimal surface of general type defined over the field K with c h a r K = p > 0 . Then we discuss the non existence of similar bounds for the dimension as K -vector space of the structural sheaf of the scheme A u t X .

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