Higher dimensional Enriques varieties with even index

Higher Dimensional Enriques Varieties with Even Index

Let Y be an Enriques variety of complex dimension 2n − 2 with n ≥ 2. Assume that n = 2m for odd prime m. In this paper we show that Y is the quotient of a product of a Calabi-Yau manifold of dimension 2m and an irreducible holomorphic symplectic manifold of dimension 2m − 2 by an automorphism of order n acting freely. We also show that both Y and its universal cover are always projective.

Codes from Higher - Dimensional Varieties

Even dimensional higher class groups of orders

Let F be a number field, and let OF denote the ring of integers in F . Let A be a finite-dimensional central simple F-algebra, and let be an OF -order in A. In this paper it is shown that the p-torsion of the even dimensional higher class group Cl2n( ) can only occur for primes p, which lie under prime ideals p, at which p is not maximal, or which divide the dimension of A.

Birational Automorphisms of Higher-dimensional Algebraic Varieties

The present survey covers the known results on the groups of birational automorphisms, rationality problem and birational classii-cation for Fano brations. 0. Birational geometry starts with M.NN other's paper 45] on Cremona transformations. The problems of birational geometry of algebraic varieties, that is, birational classiication, the rationality and unirationality problems, structure of th...

Near weights on higher dimensional varieties

We generalize the concept of near weight stated in [2007, IEEE Trans. Inform. Theory 53(5), 1919–1924] in the sense that we consider maps to arbitrary wellordered semigroups instead of the nonnegative integers. This concept can be used as a tool to study AG codes based on more than one point via elementary methods only.