Related papers: A note on Bondal's conjecture

Let \(X=G/K\) be a noncompact complex Grassmann manifold of rank \(r\). Let \(\tau_l\) be a character of \(K\), \(G\times_P{\C}\) and \(G\times_K{\C}\) the homogeneous line bundles associated with the representations…

For a torsionless connection on the tangent bundle of a manifold M the Weyl curvature W is the part of the curvature in kernel of the Ricci contraction. We give a coordinate free proof of Weyl's result that the Weyl curvature vanishes if…

Using the framework of noncommutative Kahler structures, we generalise to the noncommutative setting the celebrated vanishing theorem of Kodaira for positive line bundles. The result is established under the assumption that the associated…

A generalized version of a well-known problem of D. G. Kendall states that the zero cell of a stationary Poisson hyperplane tessellation in ${\mathbb{R}}^d$, under the condition that it has large volume, approximates with high probability a…

In this paper, we study invariant Poisson structures on homogeneous manifolds, which serve as a natural generalization of homogeneous symplectic manifolds previously explored in the literature. Our work begins by providing an algebraic…

For the universal isomonodromic deformation of an irreducible logarithmic rank two connection over a smooth complex projective curve of genus at least two, consider the family of holomorphic vector bundles over curves underlying this…

We prove that if a compact K\"ahler Poisson manifold has a symplectic leaf with finite fundamental group, then after passing to a finite \'etale cover, it decomposes as the product of the universal cover of the leaf and some other Poisson…

Let $L$ be a holomorphic line bundle on a hyperkahler manifold $M$, with $c_1(L)$ nef and not big. SYZ conjecture predicts that $L$ is semiample. We prove that this is true, assuming that $(M,L)$ has a deformation $(M',L')$ with $L'$…

We prove various results in infinite-dimensional differential calculus which relate differentiability properties of functions and associated operator-valued functions (e.g., differentials). The results are applied in two areas: 1. in the…

Let $k$ be a field. We describe necessary and sufficient conditions for a $k$-linear abelian category to be a noncommutative projective line, i.e. a noncommutative $\mathbb{P}^{1}$-bundle over a pair of division rings over $k$. As an…

The non-abelian Hodge correspondence maps a polystable $\mathrm{SL}(2,\mathbb{R})$-Higgs bundle on a compact Riemann surface $X$ of genus $g\geq2$ to a connection which, in some cases, is the holonomy of a branched hyperbolic structure. On…

We introduce the notion of lef line bundles on a complex projective manifold. We prove that lef line bundles satisfy the Hard Lefschetz Theorem, the Lefschetz Decomposition and the Hodge-Riemann Bilinear Relations. We study proper…

In earlier work we have shown that the moduli space $N$ of flat connections for the (trivial) $\roman{SU(2)}$-bundle on a closed surface of genus $\ell \geq 2$ inherits a structure of stratified symplectic space with two connected strata…

We identify the cotangent bundle Lie algebroid of a Poisson homogeneous space G/H of a Poisson Lie group G as a quotient of a transformation Lie algebroid over G. As applications, we describe the modular vector fields of G/H, and we…

We consider non-perturbative superpotentials from world-sheet instantons wrapped on holomorphic genus zero curves in heterotic string theory. These superpotential contributions feature prominently in moduli stabilization and large field…

Let M be a paracompact smooth manifold, A a Weil algebra and M^{A} the associated Weil bundle. In this paper, we give a characterization of hamiltonian field on M^{A} in the case of Poisson manifold and of Symplectic manifold.

We consider several transformation groups of a locally conformally K\"ahler manifold and discuss their inter-relations. Among other results, we prove that all conformal vector fields on a compact Vaisman manifold which is neither locally…

In this paper, we study cohomology groups of vector bundles on neighborhoods of a non-pluriharmonic locus in Stein manifolds and in projective manifolds. By using our results, we show variants of the Lefschetz hyperplane theorem.

In this paper, we show that for a given degenerate bivector $\pi= y^n\partial_x \wedge \partial_y$ with $n>1$, the classical Poisson cohomology group and the logarithmic Poisson cohomology group along the ideal…

Global properties of abelian noncommutative gauge theories based on $\star$-products which are deformation quantizations of arbitrary Poisson structures are studied. The consistency condition for finite noncommutative gauge transformations…