- Full text PDF available (59)
- This year (0)
- Last 5 years (6)
- Last 10 years (17)
Journals and Conferences
Let M be a hypercomplex Hermitian manifold, (M, I) the same manifold considered as a complex Hermitian with a complex structure I induced by the quaternions. The standard linear-algebraic construction produces a canonical nowhere degenerate (2,0)-form Ω on (M, I). It is well known that M is hyperkähler if and only if the form Ω is closed. The M is called… (More)
A locally conformally Kähler (l.c.K.) manifold is a complex manifold admitting a Kähler covering M̃ , with each deck transformation acting by Kähler homotheties. A compact l.c.K. manifold is Vaisman if it admits a holomorphic flow acting by non-trivial homotheties on M̃ . We prove a structure theorem for compact Vaisman manifolds. Every compact Vaisman… (More)
Let G be a finite group acting on a symplectic complex vector space V . Assume that the quotient V/G has a holomorphic symplectic resolution. We prove that G is generated by “symplectic reflections”, i.e. symplectomorphisms with fixed space of codimension 2 in V . Symplectic resolutions are always semismall. A crepant resolution of V/G is always symplectic.… (More)
A hypercomplex manifold is a manifold equipped with a triple of complex structures I, J,K satisfying the quaternionic relations. We define a quaternionic analogue of plurisubharmonic functions on hypercomplex manifolds, and interpret these functions geometrically as potentials of HKT (hyperkähler with torsion) metrics, and prove a quaternionic analogue of… (More)
Let (M, I) be an almost complex 6-manifold. The obstruction to integrability of almost complex structure (socalled Nijenhuis tensor) N : Λ0,1(M)−→ Λ(M) maps a 3-dimensional bundle to a 3-dimensional one. We say that Nijenhuis tensor is non-degenerate if it is an isomorphism. An almost complex manifold (M, I) is called nearly Kähler if it admits a Hermitian… (More)
Let M be a K3 surface or an even-dimensional compact torus. We show that the category of coherent sheaves on M is independent from the choice of the complex structure, if this complex structure is generic.
Let (M, I) be a compact Kähler manifold admitting a hypercomplex structure (M, I, J,K). We show that (M, I, J,K) admits a natural HKT-metric. This is used to construct a holomorphic symplectic form on (M, I).
It is well known that a Sasakian manifold is equipped with a strictly pseudoconvex CR-structure. Let M be a strictly pseudoconvex CR-manifold. We show that M admits a Sasakian metric g if and only if M admits a proper, transversal CR-holomorphic action by S, or, equivalently, an S-invariant CR-holomorphic embedding to an algebraic cone. This embedding is… (More)
We prove the Mirror Conjecture for Calabi-Yau manifolds equipped with a holomorphic symplectic form. Such man-ifolda are also known as complex manifolds of hyperkk ahler type. We obtain that a complex manifold of hyperkk ahler type is Mirror dual to itself. The Mirror Conjecture is stated (following Kontsevich, ICM talk) as the equivalence of certain… (More)
We study the deformations of a holomorphic symplectic manifold M , not necessarily compact, over a formal ring. We show (under some additional, but mild, assumptions on M) that the coarse deformation space exists and is smooth, finite-dimensional and naturally embedded into H(M). For a holomorphic symplectic manifold M which satisfies H1(OM ) = H 2(OM ) =… (More)