A few facts concerning the phrase ”the automorphism groups become larger at special points of the moduli of K3 surfaces” are presented. It is also shown that the automorphism groups are of infinite order over a dense subset in any onedimensional non-trivial family of projective K3 surfaces.

There exists a duality between elliptic curves and noncommutative tori, i.e. C∗-algebras generated by the unitary operators u and v such that vu = euv. We show that this duality can be included into a general picture involving the algebraic curves of higher genus. In this way we prove that a big part of geometry of complex algebraic curves can be developed from the K-theory of a noncommutative ...

We count points of fixed degree and bounded height on a linear projective variety defined over a number field k. If the dimension of the variety is large enough compared to the degree we derive asymptotic estimates as the height tends to infinity. This generalizes results of Thunder, Christensen and Gubler and special cases of results of Schmidt and Gao.