Results 31 to 40 of about 32,264 (146)
Sasaki structures distinguished by their basic Hodge numbers
Bulletin of the London Mathematical Society, Volume 54, Issue 5, Page 1962-1977, October 2022., 2022 Abstract In all odd dimensions at least 5 we produce examples of manifolds admitting pairs of Sasaki structures with different basic Hodge numbers. In dimension 5 we prove more precise results, for example, we show that on connected sums of copies of S2×S3$S^2\times S^3$ the number of Sasaki structures with different basic Hodge numbers within a fixed ...
D. Kotschick, G. Placini
wiley +1 more source
Journal of the London Mathematical Society, Volume 106, Issue 2, Page 590-661, September 2022., 2022 Abstract Given a generic stable strongly parabolic SL(2,C)$\operatorname{SL}(2,\mathbb {C})$‐Higgs bundle (E,φ)$({\mathcal {E}}, \varphi )$, we describe the family of harmonic metrics ht$h_t$ for the ray of Higgs bundles (E,tφ)$({\mathcal {E}}, t \varphi )$ for t≫0$t\gg 0$ by perturbing from an explicitly constructed family of approximate solutions ...
Laura Fredrickson +3 more
wiley +1 more source
Height pairing on higher cycles and mixed Hodge structures
Proceedings of the London Mathematical Society, Volume 125, Issue 1, Page 61-170, July 2022., 2022 Abstract For a smooth, projective complex variety, we introduce several mixed Hodge structures associated to higher algebraic cycles. Most notably, we introduce a mixed Hodge structure for a pair of higher cycles which are in the refined normalized complex and intersect properly. In a special case, this mixed Hodge structure is an oriented biextension,
Jose Ignacio Burgos Gil +2 more
wiley +1 more source
Dolbeault cohomology of weakly smooth forms on non-archimedean abelian varieties [PDF]
, 2023 We investigate the Dolbeault cohomology of weakly smooth forms on the Berkovich analytification of abelian varietes over a complete, non-trivially valued, non-archimedean field.
Prechtel, Miriam
core +1 more source
On the structure of double complexes
Journal of the London Mathematical Society, Volume 104, Issue 2, Page 956-988, September 2021., 2021 Abstract We study consequences and applications of the folklore statement that every double complex over a field decomposes into so‐called squares and zigzags. This result makes questions about the associated cohomology groups and spectral sequences easy to understand.
Jonas Stelzig
wiley +1 more source
Holomorphic Poisson Cohomology
Complex Manifolds, 2015 Holomorphic Poisson structures arise naturally in the realm of generalized geometry. A holomorphic Poisson structure induces a deformation of the complex structure in a generalized sense, whose cohomology is obtained by twisting the Dolbeault @-operator ...
Chen Zhuo +2 more
doaj +1 more source
Lifts of projective bundles and applications to string manifolds
Bulletin of the London Mathematical Society, Volume 53, Issue 2, Page 470-481, April 2021., 2021 Abstract We discuss the problem of lifting projective bundles to vector bundles, giving necessary and sufficient conditions for a lift to exist both in the smooth and in the holomorphic categories. These criteria are formulated and proved in the language of topology and complex differential geometry, respectively.
R. Coelho, D. Kotschick
wiley +1 more source
On the $\partial\overline{\partial}$ -Lemma and Bott-Chern cohomology [PDF]
, 2013 On a compact complex manifold X, we prove a Frölicher-type inequality for Bott-Chern cohomology and we show that the equality holds if and only if X satisfies the ...
Tomassini, Adriano +2 more
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Cohomologies of certain orbifolds [PDF]
, 2013 We study the Bott–Chern cohomology of complex orbifolds obtained as a quotient of a compact complex manifold by a finite group of ...
Angella, Daniele
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Bott–Chern cohomology and q-complete domains [PDF]
, 2013 In studying the Bott–Chern and Aeppli cohomologies for q-complete manifolds, we introduce the class of cohomologically Bott–Chern q-complete ...
Daniele Angella +3 more
core +1 more source