The Alternating Group of Degree 6 in Geometry of the Leech Lattice and K3 Surfaces
نویسنده
چکیده
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 complex algebraic geometry of K3 surfaces.
منابع مشابه
Extensions of the alternating group of degree 6 in the geometry of K3 surfaces
We shall determine the uniquely existing extension of the alternating group of degree 6 (being normal in the group) by a cyclic group of order 4, which can act on a complex K3 surface.
متن کاملNiemeier Lattices and K3 Groups Dedicated to Professor I. Dolgachev on the Occassion of His Sixtieth Birthday
In this note, we consider K3 surfaces X with an action by the alternating group A 5. We show that if a cyclic extension A 5 .C n acts on X then n = 1, 2, or 4. We also determine the A 5-invariant sublattice of the K3 lattice and its discriminant form.
متن کاملAlternating Regular Tree Grammars in the Framework of Lattice-Valued Logic
In this paper, two different ways of introducing alternation for lattice-valued (referred to as {L}valued) regular tree grammars and {L}valued top-down tree automata are compared. One is the way which defines the alternating regular tree grammar, i.e., alternation is governed by the non-terminals of the grammar and the other is the way which combines state with alternation. The first way is ta...
متن کاملSome Remarks on Brauer Groups of K3 Surfaces
We discuss the geometry of the genus one fibrations associated to an elliptic fibration on a K3 surface. We show that the two-torsion subgroup of the Brauer group of a general elliptic fibration is naturally isomorphic to the two-torsion of the Jacobian of a curve associated to the fibration. We remark that this is related to Recillas’ trigonal construction. Finally we discuss the two-torsion i...
متن کاملBirational Automorphisms of Quartic Hessian Surfaces
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 roots. A similar observation was made fir...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003