8 research outputs found
Kahlerian K3 surfaces and Niemeier lattices
Using results (especially see Remark 1.14.7) of our paper "Integral symmetric
bilinear forms and some of their applications", 1979, we clarify relation
between Kahlerian K3 surfaces and Niemeier lattices. We want to emphasise that
all twenty four Niemeier lattices are important for K3 surfaces, not only the
one which is related to the Mathieu group.Comment: Var7: 88 pages. We added last case
The Kodaira dimension of the moduli of K3 surfaces
The moduli space of polarised K3 surfaces of degree 2d is a quasi-projective
variety of dimension 19. For general d very little has been known about the
Kodaira dimension of these varieties. In this paper we present an almost
complete solution to this problem. Our main result says that this moduli space
is of general type for d>61 and for d=46,50,54,58,60.Comment: 47 page
Galois quantum systems
NoA finite quantum system in which the position and momentum take values in the Galois field GF(p¿l) is constructed from a smaller quantum system in which the position and momentum take values in Zp , using field extension. The Galois trace is used in the definition of the Fourier transform. The Heisenberg¿Weyl group of displacements and the Sp(2, GF(p¿l)) group of symplectic transformations are studied. A class of transformations inspired by the Frobenius maps in Galois fields is introduced. The relationship of this 'Galois quantum system' with its subsystems in which the position and momentum take values in subfields of GF(p¿l) is discussed