Symplectic involutions of holomorphic symplectic four-folds
نویسندگان
چکیده
منابع مشابه
Discriminant of Symplectic Involutions
We define an invariant of torsors under adjoint linear algebraic groups of type Cn—equivalently, central simple algebras of degree 2n with symplectic involution—for n divisible by 4 that takes values in H(k, μ2). The invariant is distinct from the few known examples of cohomological invariants of torsors under adjoint groups. We also prove that the invariant detects whether a central simple alg...
متن کاملHolomorphic Symplectic Geometry Ii
Hyperkähler embeddings and holomorphic symplectic geometry II. 0. Introduction. This is a second part of the treatment of complex analytic subvarieties of a holomorphically symplectic Kähler manifold. For the convenience of the reader, in the first two sections of this paper we recall the definitions and results of the first part ([V-pt I]). By Calabi-Yau theorem, the holomorphically symplectic...
متن کاملHolomorphic Triangle Invariants and the Topology of Symplectic Four-manifolds
This article analyzes the interplay between symplectic geometry in dimension four and the invariants for smooth four-manifolds constructed using holomorphic triangles introduced in [18]. Specifically, we establish a non-vanishing result for the invariants of symplectic four-manifolds, which leads to new proofs of the indecomposability theorem for symplectic four-manifolds and the symplectic Tho...
متن کاملOn the Geometry of Symplectic Involutions
Let V be a 2n-dimensional vector space over a field F and Ω be a non-degenerate symplectic form on V . Denote by Hk(Ω) the set of all 2k-dimensional subspaces U ⊂ V such that the restriction Ω|U is non-degenerate. Our main result (Theorem 1) says that if n 6= 2k and max(k, n−k) ≥ 5 then any bijective transformation of Hk(Ω) preserving the class of base subsets is induced by a semi-symplectic au...
متن کاملDeformation theory of singular symplectic n-folds
By a symplectic manifold (or a symplectic n-fold) we mean a compact Kaehler manifold of even dimension n with a non-degenerate holomorphic 2form ω, i.e. ω is a nowhere-vanishing n-form. This notion is generalized to a variety with singularities. We call X a projective symplectic variety if X is a normal projective variety with rational Gorenstein singularities and if the regular locus U of X ad...
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: Bulletin of the London Mathematical Society
سال: 2012
ISSN: 0024-6093
DOI: 10.1112/blms/bdr133