Results 31 to 40 of about 3,199 (91)

Vanishing theorems for ample vector bundles

, 1996
We prove a general vanishing theorem for the cohomology of products of symmetric and skew-symmetric powers of an ample vector bundle on a smooth complex projective variety.
Manivel, Laurent
core   +2 more sources

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
wiley   +1 more source

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
wiley   +1 more source

Holomorphic field theories and higher algebra

Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 2903-2974, October 2025.
Abstract Aimed at complex geometers and representation theorists, this survey explores higher dimensional analogs of the rich interplay between Riemann surfaces, Virasoro and Kac‐Moody Lie algebras, and conformal blocks. We introduce a panoply of examples from physics — field theories that are holomorphic in nature, such as holomorphic Chern‐Simons ...
Owen Gwilliam, Brian R. Williams
wiley   +1 more source

Calabi‐Yau Manifolds, Hermitian Yang‐Mills Instantons, and Mirror Symmetry

Advances in High Energy Physics, Volume 2017, Issue 1, 2017., 2017
We address the issue of why Calabi‐Yau manifolds exist with a mirror pair. We observe that the irreducible spinor representation of the Lorentz group Spin(6) requires us to consider the vector spaces of two forms and four forms on an equal footing. The doubling of the two‐form vector space due to the Hodge duality doubles the variety of six‐dimensional
Hyun Seok Yang, Sangheon Yun, Anna Cimmino   +2 more
wiley   +1 more source

A note on the CR cohomology of Levi-Flat minimal orbits in complex flag manifolds [PDF]

, 2005
We prove a relation between the $\bar\partial_M$ cohomology of a minimal orbit $M$ of a real form $G_0$ of a complex semisimple Lie group $G$ in a flag manifold $G/Q$ and the Dolbeault cohomology of the Matsuki dual open orbit $X$ of the complexification
Altomani, Andrea
core   +4 more sources

Dolbeault cohomology groups of compact pseudo-Kähler homogeneous manifolds

Journal of Geometry and Physics, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

Exponential actions defined by vector configurations, Gale duality, and moment‐angle manifolds

Bulletin of the London Mathematical Society, Volume 57, Issue 9, Page 2571-2629, September 2025.
Abstract Exponential actions defined by vector configurations provide a universal framework for several constructions of holomorphic dynamics, non‐Kähler complex geometry, toric geometry and topology. These include leaf spaces of holomorphic foliations, intersections of real and Hermitian quadrics, the quotient construction of simplicial toric ...
Taras Panov
wiley   +1 more source

Vanishing Theorems on Compact Hyper‐kähler Manifolds

Geometry, Volume 2014, Issue 1, 2014., 2014
We prove that if B is a k‐positive holomorphic line bundle on a compact hyper‐kähler manifold M, then Hp(M, Ωq ⊗ B) = 0 for P > n + [k/2] with q a nonnegative integer. In a special case, k = 0 and q = 0, we recover a vanishing theorem of Verbitsky’s with a little stronger assumption.
Qilin Yang, Reza Saadati
wiley   +1 more source

Bott-Chern cohomology of solvmanifolds

, 2017
We study conditions under which sub-complexes of a double complex of vector spaces allow to compute the Bott-Chern cohomology. We are especially aimed at studying the Bott-Chern cohomology of special classes of solvmanifolds, namely, complex ...
Angella, Daniele, Kasuya, Hisashi
core   +1 more source