Dolbeault cohomology of complex torus
WebAbstract. 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 … 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 …
Dolbeault cohomology of complex torus
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WebMar 5, 2012 · Complex tori that are algebraic varieties are called Abelian varieties (cf. Abelian variety). A complex torus $\C^n/\G$ is an Abelian variety if and only there exists … 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
Web开馆时间：周一至周日7:00-22:30 周五 7:00-12:00; 我的图书馆 In mathematics, in particular in algebraic geometry and differential geometry, Dolbeault cohomology (named after Pierre Dolbeault) is an analog of de Rham cohomology for complex manifolds. Let M be a complex manifold. Then the Dolbeault cohomology groups depend on a pair of integers p and q and are realized as a subquotient of the space of complex differential forms of degree (p,q).
Webany 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 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
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
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 … p type semiconductors are positively chargedWebNov 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 … p type semiconductor vs n typep type pumpsWebMar 6, 2024 · Dolbeault's theorem is a complex analog of de Rham's theorem. It asserts that the Dolbeault cohomology is isomorphic to the sheaf cohomology of the sheaf of … horse and jockey uptonWebOct 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}. p type staplesWebtorus. 3 Cohomology of complex tori Proposition 2.2 tells us that complex tori are very concrete objects to work with. Now, a natural question to ask is how the invariants of … horse and jockey walsall wood facebookWebNov 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 … horse and jockey tampa