منابع مشابه
An Isogeny of K3 Surfaces
In a recent paper Ahlgren, Ono and Penniston described the L-series of K3 surfaces from a certain one-parameter family in terms of those of a particular family of elliptic curves. The Tate conjecture predicts the existence of a correspondence between these K3 surfaces and certain Kummer surfaces related to these elliptic curves. A geometric construction of this correspondence is given here, usi...
متن کاملArithmetic of K3 surfaces
We review recent developments in the arithmetic of K3 surfaces. Our focus lies on aspects of modularity, Picard number and rational points. Throughout we emphasise connections to geometry.
متن کاملArithmetic of K3 Surfaces
Being surfaces of intermediate type, i.e., neither geometrically rational or ruled, nor of general type, K3 surfaces have a rich yet accessible arithmetic theory, which has started to come into focus over the last fifteen years or so. These notes, written to accompany a 4-hour lecture series at the 2015 Arizona Winter School, survey some of these developments, with an emphasis on explicit metho...
متن کاملK3 K3 K3 Surfaces with Involution and Analytic Torsion
In a series of works [Bo3-5], Borcherds developed a theory of modular forms over domains of type IV which admits an infinite product expansion. Such modular forms are said to be Borcherds's product in this paper. Among all Borcherds's products, Borcherds's Φ-function ([Bo4]) has an interesting geometric background; It is a modular form on the moduli space of Enriques surfaces characterizing the...
متن کاملNoncommutative K3 Surfaces
We consider deformations of a toroidal orbifold T 4/Z2 and an orbifold of quartic in CP . In the T 4/Z2 case, we construct a family of noncommutative K3 surfaces obtained via both complex and noncommutative deformations. We do this following the line of algebraic deformation done by Berenstein and Leigh for the Calabi-Yau threefold. We obtain 18 as the dimension of the moduli space both in the ...
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2006
ISSN: 0024-6093,1469-2120
DOI: 10.1112/s0024609306018170