Mathematical Proceedings of the Cambridge Philosophical Society, 2016
Using the theory of holes of the Leech lattice and Borcherds method for the computation of the au... more Using the theory of holes of the Leech lattice and Borcherds method for the computation of the automorphism group of a K3 surface, we give an effective bound for the set of isomorphism classes of projective models of fixed degree for certain K3 surfaces.
Let $Y$ be a complex Enriques surface whose universal cover $X$ is birational to a general quarti... more Let $Y$ be a complex Enriques surface whose universal cover $X$ is birational to a general quartic Hessian surface. Using the result on the automorphism group of $X$ due to Dolgachev and Keum, we obtain a finite presentation of the automorphism group of $Y$. The list of elliptic fibrations on $Y$ and the list of combinations of rational double points that can appear on a surface birational to $Y$ are presented. As an application, a set of generators of the automorphism group of the generic Enriques surface is calculated explicitly.
We investigate configurations of rational double points with the total Milnor number 21 21 on sup... more We investigate configurations of rational double points with the total Milnor number 21 21 on supersingular K 3 K3 surfaces. The complete list of possible configurations is given. As an application, we also give the complete list of extremal (quasi-)elliptic fibrations on supersingular K 3 K3 surfaces.
We determine all possible configurations of rational double points on complex normal algebraic K3... more We determine all possible configurations of rational double points on complex normal algebraic K3 surfaces, and on normal supersingular K3 surfaces in characteristic p > 19.
Mathematical Proceedings of the Cambridge Philosophical Society, 2016
Using the theory of holes of the Leech lattice and Borcherds method for the computation of the au... more Using the theory of holes of the Leech lattice and Borcherds method for the computation of the automorphism group of a K3 surface, we give an effective bound for the set of isomorphism classes of projective models of fixed degree for certain K3 surfaces.
Let $Y$ be a complex Enriques surface whose universal cover $X$ is birational to a general quarti... more Let $Y$ be a complex Enriques surface whose universal cover $X$ is birational to a general quartic Hessian surface. Using the result on the automorphism group of $X$ due to Dolgachev and Keum, we obtain a finite presentation of the automorphism group of $Y$. The list of elliptic fibrations on $Y$ and the list of combinations of rational double points that can appear on a surface birational to $Y$ are presented. As an application, a set of generators of the automorphism group of the generic Enriques surface is calculated explicitly.
We investigate configurations of rational double points with the total Milnor number 21 21 on sup... more We investigate configurations of rational double points with the total Milnor number 21 21 on supersingular K 3 K3 surfaces. The complete list of possible configurations is given. As an application, we also give the complete list of extremal (quasi-)elliptic fibrations on supersingular K 3 K3 surfaces.
We determine all possible configurations of rational double points on complex normal algebraic K3... more We determine all possible configurations of rational double points on complex normal algebraic K3 surfaces, and on normal supersingular K3 surfaces in characteristic p > 19.
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