Dolbeault cohomology of complex torus
WebRoman Krutowski and Taras Panov – Dolbeault cohomology of complex manifolds with torus action Eunjeong Lee, Mikiya Masuda, Seonjeong Park and Jongbaek Song – Poincaré polynomials of generic torus orbit closures in Schubert varieties Ivan Limonchenko and Dmitry Millionshchikov – Higher order Massey products and applications WebHere are a couple of ideas for doing this. (1) A complex torus is a Kahler manifold, since any flat metric on Euclidean space is invariant under the action of the lattice that defines the …
Dolbeault cohomology of complex torus
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Webfor the Cohomology of Invertible Sheaves Let X = V / L be a complex torus. Let (0:, H) be A.-H. data. Let A ° be the space of all Coo sections of !L'(o:,H). Thus AO consists of all … WebMay 26, 2024 · induces a surjection on Dolbeault cohomology. \(\square \) Corollary 4.3. Let M be a compact complex manifold and K a connected compact Lie group acting on M as biholomorphisms. Let H be a dense Lie subgroup of K such that H is a complex Lie group and the restricted action of K to H on M is holomorphic. Then, the inclusion …
Web3 Equivariant Dolbeault cohomology Suppose that M =(M;J) is a compact complex manifold and G acts on M holomorphically. In this section, we present an equivariant version of the Dolbeault cohomology on M following the outline given in [Lil03, Theorem 5.1]. Recall from complex geometry that the complexification of the cotangent bundle TM …
WebWe describe the basic Dolbeault cohomology algebra of the canonical foliation on a class of complex manifolds with a torus symmetry group. This class includes complex moment-angle manifolds, LVM ... WebDolbeault cohomology of complex tori. Asked 12 years, 5 months ago Modified 10 years, 2 months ago Viewed 2k times 11 Let T = C n / Λ a complex torus. It is completely …
WebAug 18, 2024 · Abstract: We describe the basic Dolbealut cohomology algebra of the canonical foliation on a class of complex manifolds with a torus symmetry group. This …
WebSep 1, 1999 · It is a well-known classical result that on a complex torus, i.e. a quotient of C by a lattice of maximal rank 2«, every divisor is the divisor of a theta function. In this ... we calculate in section 1 the Dolbeault cohomology groups of a toroidal group … Expand. 28. Save. Alert. On completeness of holomorphic principal bundles. S. Takeuchi ... parker thomasWebof bigraded differential forms which define the de Rham and the Dolbeault cohomology groups (for a fixed p ∈ N) respectively: H dR(Z,C) ∶= kerd imd and Hp, (Z,∂¯) ∶= ker∂¯ im∂¯ Theorem 2.6 (Theorem 3.4.4 in [4] and Theorem 1.2 in [1] ). Let Z be a compact complex orbifold. There are natural isomorphisms: 3 timeweaveWebJan 30, 2024 · We study the existence of non-trivial Abelian J-invariant ideals \({\mathfrak f}\) in nilpotent Lie algebras \({\mathfrak g}\) endowed with a complex structure J.This condition appears as one of the hypotheses in a recent theorem by A. Fino, S. Rollenske and J. Ruppenthal on the Dolbeault cohomology of complex nilmanifolds. parker thomas moonWebNov 19, 2024 · It generalizes the Dolbeault cohomology of complex manifolds, since in the integrable case, for which μ ¯ ≡ 0, the cohomology H μ ¯ ⁎, ⁎ (M) is the space of all … parker thomas hockeyWebAbstract. We describe the basic Dolbeault cohomology algebra of the canonical foliation on a class of complex manifolds with a torus symme-try group. This class includes complex moment-angle manifolds, LVM-and LVMB-manifolds and, in most generality, complex manifolds with a maximal holomorphic torus action. We also provide a dga … parker thomas ruchWebDolbeault cohomology of complex manifolds with torus action RomanKrutowskiandTarasPanov Abstract. … parker threaded cartridge valvesWebany complex manifold with a maximal torus action is transverse equivalent to a complex moment-angle manifold (Theorem 5.8). This gives a description of the basic cohomology ring for any complex manifold with a maximal torus action (Theorem 5.10). Since LVMB manifolds are a particular class of maximal torus actions, the conjecture of Battaglia and parker thomas hats denver