Results 11 to 20 of about 3,199 (91)
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
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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
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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
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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
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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
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Duality of Hodge numbers of compact complex nilmanifolds
Complex Manifolds, 2015 A compact K¨ahlerian manifoldM of dimension n satisfies hp,q(M) = hq,p(M) for each p, q.However, a compact complex manifold does not satisfy the equations in general. In this paper, we consider duality of Hodge numbers of compact complex nilmanifolds.
Yamada Takumi
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Hodge numbers and invariant complex structures of compact nilmanifolds
Complex Manifolds, 2016 In this paper, we consider several invariant complex structures on a compact real nilmanifold, and we study relations between invariant complex structures and Hodge numbers.
Yamada Takumi
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Remarks on Hodge numbers and invariant complex structures of compact nilmanifolds
Complex Manifolds, 2016 If N is a simply connected real nilpotent Lie group with a Γ-rational complex structure, where Γ is a lattice in N, then for each s, t.We study relations between invariant complex structures and Hodge numbers of compact nilmanifolds from a ...
Yamada Takumi
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F‐Manifolds and geometry of information
Bulletin of the London Mathematical Society, Volume 52, Issue 5, Page 777-792, October 2020., 2020 Abstract The theory of F‐manifolds, and more generally, manifolds endowed with commutative and associative multiplication of their tangent fields, was discovered and formalised in various models of quantum field theory involving algebraic and analytic geometry, at least since the 1990s. The focus of this paper consists in the demonstration that various
Noémie Combe, Yuri I. Manin
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Some relations between Hodge numbers and invariant complex structures on compact nilmanifolds
Complex Manifolds, 2017 Let N be a simply connected real nilpotent Lie group, n its Lie algebra, and € a lattice in N. If a left-invariant complex structure on N is Γ-rational, then HƏ̄s,t(Γ/N) ≃ HƏ̄s,t(nC) for each s; t.
Yamada Takumi
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