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Journals and Conferences
We find generators of the group of birational automorphisms of the Hessian surface of a general cubic surface. Its nonsingular minimal model is a K3 surface with the Picard lattice of rank 16 which embeds naturally in the even unimodular lattice II1,25 of rank 26 and signature (1, 25). The generators are related to reflections with respect to some Leech… (More)
First, we formulate and prove Theorem of Lie-Kolchin type for a cone and derive some algebro-geometric consequences. Next, inspired by a recent result of Dinh and Sibony we pose a conjecture of Tits type for a group of automorphisms of a complex variety and verify its weaker version. Finally, applying Theorem of Lie-Kolchin type for a cone, we confirm the… (More)
A fake projective plane is a compact complex surface (a compact complex manifold of dimension 2) with the same Betti numbers as the complex projective plane, but not isomorphic to the complex projective plane. As was shown by Mumford, there exists at least one such surface. In this paper we prove the existence of a fake projective plane which is birational… (More)
We investigate when the fundamental group of the smooth part of a K3 surface or Enriques surface with Du Val singularities, is finite. As a corollary we give an effective upper bound for the order of the fundamental group of the smooth part of a certain Fano 3-fold. This result supports Conjecture A below, while Conjecture A (or alternatively the… (More)
The alternating group of degree 6 is located at the junction of three series of simple non-commutative groups : simple sporadic groups, alternating groups and simple groups of Lie type. It plays a very special role in the theory of finite groups. We shall study its new roles both in a finite geometry of certain pentagon in the Leech lattice and also in a… (More)
We classify possible finite groups of symplectic automorphisms of K3 surfaces of order divisible by 11. The characteristic of the ground field must be equal to 11. The complete list of such groups consists of five groups: the cyclic group C11 of order 11, C11 o C5, PSL2(F11) and the Mathieu groups M11, M22. We also show that a surface X admitting an… (More)
We calculate the automorphism groups of several Kummer surfaces associated with the product of two elliptic curves. We give their generators explicitly.
In this paper we study automorphisms g of order p of K3-surfaces defined over an algebraically closed field of characteristic p > 0. We divide all possible actions in the following cases according to the structure of the set of fixed points X: X is a finite set, X contains a one-dimensional part D which is a positive divisor of Kodaira dimension κ(X,D) = 0,… (More)
Kollár’s conjecture states that a complex projective surface S with quotient singularities and with H(S, Q) = Q should be rational if its smooth part S is simply connected. We confirm the conjecture under the additional condition that the exceptional divisor in a minimal resolution of S has at most 3 components over each singular point of S.
Recently, Prasad and Yeung classified all possible fundamental groups of fake projective planes. According to their result, many fake projective planes admit a nontrivial group of automorphisms, and in that case it is isomorphic to Z/3Z, Z/7Z, 7 : 3, or (Z/3Z), where 7 : 3 is the unique non-abelian group of order 21. Let G be a group of automorphisms of a… (More)