Hyper-Kähler fourfolds and Kummer surfaces
نویسندگان
چکیده
منابع مشابه
Kähler (& Hyper-kähler) Manifolds
These notes are based on two talks given at the Arithmetic & Algebraic Geometry Seminar of the Korteweg-de Vriesinstituut for mathematics of the Universiteit van Amsterdam. They are intended to give a short introduction to the theory of Kähler manifolds, with a slight focus of applicability to the subject of K3 surfaces. However, they also include other interesting results not related to K3 sur...
متن کاملHodge Theory and Lagrangian Planes on Generalized Kummer Fourfolds
Suppose X is a smooth projective complex variety. Let N1(X,Z) ⊂ H2(X,Z) and N(X,Z) ⊂ H(X,Z) denote the group of curve classes modulo homological equivalence and the Néron-Severi group respectively. The monoids of effective classes in each group generate cones NE1(X) ⊂ N1(X,R) and NE(X) ⊂ N(X,R) with closures NE1(X) and NE 1 (X), the pseudoeffective cones. These play a central rôle in the birati...
متن کاملHodge Theory and Lagrangian Planes on Generalized Kummer Fourfolds
Suppose X is a smooth projective complex variety. Let N1(X,Z) ⊂ H2(X,Z) and N(X,Z) ⊂ H(X,Z) denote the group of curve classes modulo homological equivalence and the Néron-Severi group respectively. The monoids of effective classes in each group generate cones NE1(X) ⊂ N1(X,R) and NE(X) ⊂ N(X,R) with closures NE1(X) and NE 1 (X), the pseudoeffective cones. These play a central rôle in the birati...
متن کاملHyper-kähler Fourfolds Fibered by Elliptic Products
Every fibration of a projective hyper-Kähler fourfold has fibers which are Abelian surfaces. In case the Abelian surface is a Jacobian of a genus two curve, these have been classified by Markushevich. We classify those cases where the Abelian surface is a product of two elliptic curves, under some mild genericity hypotheses. Unlike the genus two case, we prove there are infinitely many deformat...
متن کاملKähler Surfaces And
A complex ruled surface admits an iterated blow-up encoded by a parabolic structure with rational weights. Under a condition of parabolic stability, one can construct a Kähler metric of constant scalar curvature on the blow-up according to [18]. We present a generalization of this construction to the case of parabolically polystable ruled surfaces. Thus we can produce numerous examples of Kähle...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2017
ISSN: 0024-6115
DOI: 10.1112/plms.12063