Dolbeault cohomology of complex torus

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August undefined, 2024

WebAs a natural generalization, one can replace the circle with a two-dimensional torus. This leads to Witten's proposal for the index of Dirac operators on loop spaces, which is still a mystery in geometry and topology. See Full PDF Download PDF. ... equivariant cohomology and topological field theories. 1995 • Sanjaye Ramgoolam. Download Free ... WebJan 1, 2001 · We deal with the classi_cation problem of compact nilmanifolds admitting such a _ , the study of a Dolbeault minimal model and its formality, and the construction of nilpotent complex structures ...

arXiv:1908.06356v4 [math.DG] 31 Aug 2024

WebAbstract. A nilmanifold is a quotient of a nilpotent group G by a co-compact discrete subgroup. A complex nilmanifold is one which is equipped with a G-invariant complex structure WebFeb 17, 2024 · As applications, we obtain various refinements of the homotopy groups, sensitive to the complex structure. Under a simple connectedness assumption, one obtains minimal models which are unique up... cizme franjuri

An introduction to equivariant cohomology and the …

Webto 0) as an evaluation of cohomology classes over the reduced space at 0. This formula exhibits the dependence of the Riemann-Roch number on Λ. We also express the for-mula as a sum over the components of the ﬁxed point set of the maximal torus. Our proof applies to Hamiltonian G-manifolds even if they do not have a compatible K¨ahler WebUsing G2(2) dualities we construct the most general black string solution of minimal five-dimensional ungauged supergravity. The black string has five independent parameters, namely, the magnetic one-brane charge, smeared electric zero-brane charge, boost along the string direction, energy above the BPS bound, and rotation in the transverse space. WebAug 17, 2024 · We describe the basic Dolbealut cohomology algebra of the canonical foliation on a class of complex manifolds with a torus symmetry group. This class … cizme de zapada

Dolbeault cohomology of complex tori. - MathOverflow

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WebNov 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 … WebWe show that ifM is the total space of a holomorphic bundle with base space a simply connected homogeneous projective variety and fibre and structure group a compact … cizme gaerneWebJun 28, 2000 · theorem for the Dolbeault cohomology of a compact complex parallelizable nilman-ifold nG; but there exist many interesting compact nilmanifolds with a nilpotent complex structure which are not complex parallelizable but only real parallelizable (see Examples 2{4 in Section 5). Our purpose is to prove the following theorem. Main Theorem. cizme glami

"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 … " - Dolbeault cohomology of complex torus

Dolbeault cohomology of complex torus

Taras PANOV Professor Doctor of Science, PhD - ResearchGate

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 … WebIf Mis a complex manifold andTacts via holomorphic transformations, a Dolbeault version of T-equivariant cohomology is constructed in a similar way. For x2Lie(T), let V x= W x+W xbe the splitting of the generating vec-tor eld of xinto holomorphic and anti-holomorphic components. Imitating the Cartan construction, let Ap; T (M) be the complex of ...

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WebJan 19, 2024 · In particular, every complex torus is a Kähler manifold. Any one-dimensional complex manifold is Kählerian. The theory of harmonic forms on a compact Kähler manifold $ M $ yields the following properties of the de Rham and Dolbeault cohomology groups on $ … WebMay 23, 2010 · After calculating the differential, my answer is that this decomposes as a dot at each corner, a zigzag of length 3 next to each each corner, and a progression of squares. Modulo the conjecture that all zigzags are invariant, this is a complete description of the Dolbeault complex.

WebNov 1, 2024 · Let G be a complex Lie group acting on a compact complex Hermitian manifold M by holomorphic isometries. We prove that the induced action on the … 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

Webof 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 WebIn this paper we give an account of the very basics of equivariant de Rham and Dolbeault cohomology and the equivariant ﬁrst Chern class, which lies at the foundation of …

WebNilmanifolds with left-invariant complex structure 6 1.3. Dolbeault cohomology of nilmanifolds and small deformations 11 1.4. Examples and Counterexamples 12 2. Albanese-Quotients and deformations in the large 15 ... complex torus is again a complex torus has been fully proved only in 2002 by Catanese [Cat02]. In [Cat04] he studies …

WebOct 21, 2014 · 3 Class VII surfaces. In this section, we compute Bott-Chern cohomology for compact complex surfaces in class \text {VII}. Let X be a compact complex surface. By Theorem 1.1, the natural map H^ {2,1}_ {BC} (X) \rightarrow H^ {2,1}_ {\overline {\partial }} (X) is always injective. Consider now the case when X is in class \text {VII}. cizme lungi dama zapatosWebJan 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. cizme grenaWebWe 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 ... cizme kamikWebfor 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 … cizme janaWebWe prove a Bochner type vanishing theorem for compact complex manifolds in Fujiki class , with vanishing first Chern class, that admit a cohomology class which is numerically effective (nef) and has positive self-int… cizme griWebThe study of the Dolbeault cohomology of complex nilmanifolds is motivated by the fact that nilmanifolds provide examples of symplectic manifolds with no Kähler structure. … cizme mihaela glavanWebDolbeault Cohomology is invariant under homeomorphisms. If X and Y are two complex manifolds, which are homeomorphic but not necessarily diffeomorphic, must their … cizme liu jo