Results 51 to 60 of about 32,264 (146)
Computations of generalized Dolbeault cohomology
AIP Conference Proceedings, 2009 We study the (generalized Dolbeault) cohomology of generalized complex manifolds in 4 real dimensions. We show that in 4 real dimensions, the first cohomology around a nondegenerate type change point is given by holomorphic (1,0) forms defined on the type change locus.
Gil R. Cavalcanti +4 more
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TWISTED DOLBEAULT COHOMOLOGY OF NILPOTENT LIE ALGEBRAS
Transformation Groups, 2020 It is well known that cohomology of any non-trivial 1-dimensional local system on a nilmanifold vanishes (this result is due to L. Alaniya). A complex nilmanifold is a quotient of a nilpotent Lie group equipped with a left-invariant complex structure by an action of a discrete, co-compact subgroup.
Ornea, Liviu, Verbitsky, Misha
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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
wiley +1 more source
Quiver indices and Abelianization from Jeffrey-Kirwan residues
Journal of High Energy Physics, 2019 In quiver quantum mechanics with 4 supercharges, supersymmetric ground states are known to be in one-to-one correspondence with Dolbeault cohomology classes on the moduli space of stable quiver representations.
Guillaume Beaujard +2 more
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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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Complex structures on the complexification of a real Lie algebra
Complex Manifolds, 2018 Let g = a+b be a Lie algebra with a direct sum decomposition such that a and b are Lie subalgebras. Then, we can construct an integrable complex structure J̃ on h = ℝ(gℂ) from the decomposition, where ℝ(gℂ) is a real Lie algebra obtained from gℂby the ...
Yamada Takumi
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Hodge theory for twisted differentials
Complex Manifolds, 2014 We study cohomologies and Hodge theory for complex manifolds with twisted differentials. In particular, we get another cohomological obstruction for manifolds in class C of Fujiki. We give a Hodgetheoretical proof of the characterization of solvmanifolds
Angella Daniele, Kasuya Hisashi
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Frobenius manifold structure on Dolbeault cohomology and mirror symmetry [PDF]
Communications in Analysis and Geometry, 2000 We construct a differential Gerstenhaber-Batalin-Vilkovisky algebra from Dolbeault complex of any close Kaehler manifold, and a Frobenius manifold structure on Dolbeault cohomology.
Cao, Huai-Dong, Zhou, Jian
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Fortschritte der Physik, Volume 74, Issue 4, April 2026.ABSTRACT In this paper, we continue the development of the Cartan neural networks programme, launched with three previous publications, by focusing on some mathematical foundational aspects that we deem necessary for our next steps forward. The mathematical and conceptual results are diverse and span various mathematical fields, but the inspiring ...
Pietro Fré +4 more
wiley +1 more source
Bott-Chern cohomology of solvmanifolds [PDF]
, 2012 We study conditions under which sub-complexes of a double complex of vector spaces allow to compute the Bott-Chern cohomology.
Daniele Angella +3 more
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