Results 1 to 10 of about 19 (19)
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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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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Canonical complex extensions of Kähler manifolds
Journal of the London Mathematical Society, Volume 101, Issue 2, Page 786-827, April 2020., 2020 Abstract Given a complex manifold X, any Kähler class defines an affine bundle over X, and any Kähler form in the given class defines a totally real embedding of X into this affine bundle. We formulate conditions under which the affine bundles arising this way are Stein and relate this question to other natural positivity conditions on the tangent ...
Daniel Greb, Michael Lennox Wong
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Type IIB Flux Vacua and Tadpole Cancellation
Fortschritte der Physik, Volume 67, Issue 11, November 2019., 2019 Abstract We consider flux vacua for type IIB orientifold compactifications and study their interplay with the tadpole‐cancellation condition. As a concrete example we focus on , for which we find that solutions to the F‐term equations at weak coupling, large complex structure and large volume require large flux contributions.
Philip Betzler, Erik Plauschinn
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Topological K‐theory of quasi‐BPS categories for Higgs bundles
Journal of Topology, Volume 18, Issue 4, December 2025.Abstract In a previous paper, we introduced quasi‐BPS categories for moduli stacks of semistable Higgs bundles. Under a certain condition on the rank, Euler characteristic, and weight, the quasi‐BPS categories (called BPS in this case) are noncommutative analogues of Hitchin integrable systems.
Tudor Pădurariu, Yukinobu Toda
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Moduli Space in Homological Mirror Symmetry
Advances in Mathematical Physics, Volume 2019, Issue 1, 2019., 2019 We prove that the moduli space of the pseudo holomorphic curves in the A‐model on a symplectic torus is homeomorphic to a moduli space of Feynman diagrams in the configuration space of the morphisms in the B‐model on the corresponding elliptic curve. These moduli spaces determine the A∞ structure of the both models.
Matsuo Sato, Dimitrios Tsimpis
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