Trianalytic subvarieties of the Hilbert scheme of points on a K 3 surface
نویسنده
چکیده
Let X be a hyperkähler manifold. Trianalytic subvarieties of X are subvarieties which are complex analytic with respect to all complex structures induced by the hyperkähler structure. Given a K3 surface M , the Hilbert scheme classifying zero-dimensional subschemes of M admits a hy-perkähler structure. We show that for M generic, there are no trianalytic subvarieties of the Hilbert scheme. This implies that a generic deformation of the Hilbert scheme of K3 has no proper complex subvarieties.
منابع مشابه
Equilibrium problems and fixed point problems for nonspreading-type mappings in hilbert space
In this paper by using the idea of mean convergence, weintroduce an iterative scheme for finding a common element of theset of solutions of an equilibrium problem and the fixed points setof a nonspreading-type mappings in Hilbert space. A strongconvergence theorem of the proposed iterative scheme is establishedunder some control conditions. The main result of this paper extendthe results obtain...
متن کاملApproximation of fixed points for a continuous representation of nonexpansive mappings in Hilbert spaces
This paper introduces an implicit scheme for a continuous representation of nonexpansive mappings on a closed convex subset of a Hilbert space with respect to a sequence of invariant means defined on an appropriate space of bounded, continuous real valued functions of the semigroup. The main result is to prove the strong convergence of the proposed implicit scheme to the unique solutio...
متن کاملDeformations of Trianalytic Subvarieties Deformations of Trianalytic Subvarieties of Hyperkk Ahler Manifolds
Let M be a compact complex manifold equipped with a hyperkk ahler metric, and X be a closed complex analytic subvariety of M. In alg-geom 9403006, we proved that X is trianalytic (i. e., complex analytic with respect to all complex structures induced by the hyperkk ahler structure), provided that M is generic in its deformation class. Here we study the complex analytic deformations of trian-aly...
متن کاملSubvarieties in non-compact hyperkähler manifolds
Let M be a hyperkähler manifold, not necessarily compact, and S ∼= CP 1 the set of complex structures induced by the quaternionic action. Trianalytic subvariety of M is a subvariety which is complex analytic with respect to all I ∈ CP . We show that for all I ∈ S outside of a countable set, all compact complex subvarieties Z ⊂ (M, I) are trianalytic. For M compact, this result was proven in [V1...
متن کاملDeformations of trianalytic subvarieties of hyperkähler manifolds
Let M be a compact complex manifold equipped with a hyperkähler metric, and X be a closed complex analytic subvariety of M. In alg-geom 9403006, we proved that X is trianalytic (i. e., complex analytic with respect to all complex structures induced by the hyperkähler structure), provided that M is generic in its deformation class. Here we study the complex analytic deformations of trian-alytic ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997