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Journal Article
The Journal of geometric analysis, ISSN 1559-002X, 2019, Volume 30, Issue 1, pp. 493 - 510
We view Dolbeault-Morse-Novikov cohomology H eta p,q(X) as the cohomology of the sheaf Omega X,eta p of eta-holomorphic p-forms and give several bimeromorphic invariants... 
Bimeromorphic | Sheaf of eta-holomorphic functions | Blow-up formula | Stability | Leray-Hirsch theorem | eta-hodge number | BLOW-UPS | Dolbeault-Morse-Novikov cohomology | MATHEMATICS | Weight theta-sheaf | theta-betti number | DOLBEAULT COHOMOLOGY | Morse-Novikov cohomology
Journal Article
International journal of mathematics, ISSN 1793-6519, 2014, Volume 25, Issue 6, pp. 1450057 - 1-1450057-24
The Bott–Chern cohomology of six-dimensional nilmanifolds endowed with invariant complex structure is studied with special attention to the cases when balanced or strongly Gauduchon Hermitian metrics exist... 
Bott-chern cohomology | Holomorphic deformation | Complex structure | Nilmanifold | MATHEMATICS | SMALL DEFORMATIONS | complex structure | DOLBEAULT-COHOMOLOGY | Bott-Chern cohomology | holomorphic deformation | STABILITY | MANIFOLDS | COMPLEX STRUCTURES | GEOMETRY | Balancing | Deformation | Mathematical analysis | Supergravity | Invariants
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 07/2015, Volume 93, pp. 52 - 61
We study a geometric notion related to formality for Bott–Chern cohomology on complex manifolds. 
Complex manifold | Hermitian metric | Cohomology | Formality | Bott–Chern cohomology | Bott-Chern cohomology | MATHEMATICS | COMPLEX | SOLVMANIFOLDS | MANIFOLDS | DOLBEAULT COHOMOLOGY | PHYSICS, MATHEMATICAL | Bott-Chem cohomology | HOMOTOPY THEORY
Journal Article
by Liu, YF
ALGEBRAIC GEOMETRY, ISSN 2313-1691, 07/2019, Volume 6, Issue 4, pp. 384 - 409
We define monodromy maps for the tropical Dolbeault cohomology of algebraic varieties over non-Archimedean fields... 
MATHEMATICS | tropical Dolbeault cohomology | monodromy map
Journal Article
Quarterly Journal of Mathematics, ISSN 0033-5606, 2017, Volume 68, Issue 3, pp. 705 - 728
We study quaternionic Bott-Chern cohomology on compact hypercomplex manifolds and adapt some results from complex geometry to the quaternionic setting... 
MATHEMATICS | INVARIANT COMPLEX STRUCTURE | BUNDLES | KAHLER | TORSION | MANIFOLDS | DOLBEAULT COHOMOLOGY | COMPACT NILMANIFOLDS | SURFACES | GEOMETRY | Mathematics - Differential Geometry
Journal Article
Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2018, Volume 70, Issue 1, pp. 409 - 422
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 09/2013, Volume 71, pp. 117 - 126
We study the Bott–Chern cohomology of complex orbifolds obtained as a quotient of a compact complex manifold by a finite group of biholomorphisms. 
[formula omitted]-lemma | Orbifolds | Bott–Chern cohomology | Bott-Chern cohomology | lemma | partial derivative partial derivative-lemma | HOLONOMY SPIN | MATHEMATICS, APPLIED | COMPACT 8-MANIFOLDS | MANIFOLDS | PHYSICS, MATHEMATICAL | DOLBEAULT | Mathematics - Differential Geometry
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 2/2013, Volume 273, Issue 1, pp. 437 - 447
... such that N are nilpotent Lie groups with left-invariant complex structures. We compute the Dolbeault cohomology of direct sums of holomorphic line bundles over G/Γ... 
22E25 | 53C30 | Dolbeault cohomology | Solvmanifold | 53C55 | Mathematics, general | Invariant complex structure | Holomorphic line bundle | Mathematics | MATHEMATICS | COMPACT NILMANIFOLDS | Methods | Algebra
Journal Article
Annals of Global Analysis and Geometry, ISSN 0232-704X, 3/2017, Volume 51, Issue 2, pp. 155 - 177
Journal Article
Mathematical Research Letters, ISSN 1073-2780, 2014, Volume 21, Issue 4, pp. 781 - 805
...". By this result, we construct an explicit finite-dimensional cochain complex which compute the cohomology H*(G/Gamma, E... 
De Rham cohomology | Dolbeault cohomology | Local system | Solvmanifold | Lie algebra cohomology | MATHEMATICS | solvmanifold | LIE-GROUPS | de Rham cohomology | local system | POLYNOMIAL STRUCTURES
Journal Article
Differential Geometry and its Applications, ISSN 0926-2245, 02/2016, Volume 44, pp. 144 - 160
.... As a basic fact, we establish that on such manifolds, the Dolbeault cohomology with coefficients in holomorphic polyvector fields is isomorphic to the cohomology of invariant forms with coefficients... 
Abelian complex structure | Spectral sequence | Holomorphic Poisson structure | Nilmanifold | MATHEMATICS, APPLIED | DOLBEAULT-COHOMOLOGY | COMPACT NILMANIFOLDS | MATHEMATICS | ALGEBRAS | DEFORMATIONS | MANIFOLDS | GENERALIZED COMPLEX STRUCTURES | GEOMETRY
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 8/2013, Volume 274, Issue 3, pp. 1165 - 1176
...Math. Z. (2013) 274:1165–1176 DOI 10.1007/s00209-012-1111-z Mathematische Zeitschrift On the Hausdorff property of some Dolbeault cohomology groups Christine... 
32C35 | Dolbeault cohomology | Separation | Mathematics, general | Mathematics | Duality | 32C37 | MATHEMATICS | SERRE DUALITY | OPERATOR | REGULARITY | MANIFOLDS
Journal Article
The Journal of Geometric Analysis, ISSN 1050-6926, 1/2017, Volume 27, Issue 1, pp. 142 - 161
Journal Article
中国科学:数学英文版, ISSN 1674-7283, 2017, Volume 60, Issue 6, pp. 949 - 962
The main purpose of this paper is to generalize the celebrated L2 extension theorem of Ohsawa and Takegoshi in several directions: The holomorphic sections to... 
plurisubharmonic function | compact Kähler manifold | Dolbeault cohomology | coherent sheaf cohomology | singular hermitian metric | multiplier ideal sheaf | Ohsawa-Takegoshi extension theorem | estimates | MATHEMATICS | L-2 estimates | MATHEMATICS, APPLIED | compact Kahler manifold
Journal Article
Annali della Scuola normale superiore di Pisa - Classe di scienze, ISSN 0391-173X, 2011, Volume 10, Issue 4, pp. 801 - 818
...] on the de Rham cohomology of a compact solvmanifold, i.e., of a quotient of a connected and simply connected solvable Lie group G by a lattice Gamma... 
SPLITTINGS | MATHEMATICS | DOLBEAULT-COHOMOLOGY | SOLVABLE LIE-GROUPS | HOMOGENEOUS SPACES | MANIFOLDS | NILMANIFOLDS
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 2017, Volume 145, Issue 1, pp. 273 - 285
We introduce a "qualitative property" for Bott-Chern cohomology of complex non-Kahler manifolds, which is motivated in view of the study of the algebraic structure of Bott-Chern cohomology... 
Complex manifold | Bott-Chern cohomology | Non-Kähler geometry | Lemma | Aeppli cohomology | non-Kahler geometry | MATHEMATICS | MATHEMATICS, APPLIED | COMPLEX | HODGE THEORY | partial derivative partial derivative-Lemma | DOLBEAULT | HOMOTOPY THEORY
Journal Article
Journal of Geometric Analysis, ISSN 1050-6926, 7/2013, Volume 23, Issue 3, pp. 1355 - 1378
We prove that, for some classes of complex nilmanifolds, the Bott–Chern cohomology is completely determined by the Lie algebra associated with the nilmanifold with the induced complex structure... 
Iwasawa manifold | Bott–Chern | Deformations | Solvmanifold | Mathematics | 53C15 | Cohomology | 32G05 | Abstract Harmonic Analysis | Fourier Analysis | 57T15 | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | Bott-Chern | MATHEMATICS | INVARIANT COMPLEX STRUCTURE | KAHLER MANIFOLDS | DOLBEAULT COHOMOLOGY | COMPACT NILMANIFOLDS | Algebra | Mathematics - Differential Geometry
Journal Article
AIP Conference Proceedings, ISSN 0094-243X, 2009, Volume 1093, Issue 1, pp. 57 - 69
We study the (generalized Dolbeault) cohomology of generalized complex manifolds in 4 real dimensions... 
Generalized complex structures | Dolbeault cohomology | COMPLEX MANIFOLDS | NUMERICAL ANALYSIS | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | SUPERGRAVITY | CALCULATION METHODS | QUANTUM FIELD THEORY | GAUGE INVARIANCE
Conference Proceeding
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