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Cyclic groups of automorphisms of complex K3 surfaces
Cyclic groups automorphisms complex K3 surfaces
2012/2/29
We determine all possible orders of automorphisms of complex K3 surfaces. A positive integer N is the order of an automorphism of a complex K3 surface if and only if \phi(N) \leq 20 and N is not 60, w...
On the existence of curves with $A_k$-singularities on $K3$-surfaces
versal deformations tacnodes Severi varieties K3 surfaces Ak-singularities
2011/9/19
Abstract: Let $(S,H)$ be a general primitively polarized $K3$ surface. We prove the existence of curves in $|\mathcal O_S(nH)|$ with $A_k$-singularities and corresponding to regular points of the equi...
A note on exceptional unimodal singularities and K3 surfaces
exceptional unimodal singularities K3 surfaces note Algebraic Geometry
2011/9/1
Abstract: This is a short note on the relation between the graded stable derived categories of 14 exceptional unimodal singularities and the derived category of K3 surfaces obtained as compactificatio...
Finiteness of K3 surfaces and the Tate conjecture
K3 surfaces the Tate conjecture Algebraic Geometry Number Theory
2011/8/26
Abstract: Given a finite field k of characteristic at least 5, we show that the Tate conjecture holds for K3 surfaces defined over the algebraic closure of k if and only if there are only finitely man...