arXiv research

Stable Higgs bundles on elliptic fibrations are decomposed into simpler components.

We consider the notion of stable isomorphism of bundle gerbes. It has the consequence that the stable isomorphism classes of bundle gerbes over a manifold M are in bijective correspondence with H^3(M, Z). Stable isomorphism sheds light on the local theory of bundle gerbes and enables us to develop a classifying theory …

Study on stable vector bundles over Gauduchon manifolds.

The paper solves equations for Higgs bundles on non-Kähler manifolds.

Polystable bundles on Kaehler manifolds are stable if their classes are stable.

Construct Hermitian-Einstein metrics on stable holomorphic vector bundles using dynamical methods.

We investigate Chow stability of projective bundles P(E) where E is a strictly Gieseker stable bundle over a base manifold that has constant scalar curvature. We show that, for suitable polarisations L, the pair (P(E),L) is Chow stable and give examples for which it is not asymptotically Chow stable.

Projectively flat bundles matched with semi-stable Higgs bundles on Kähler manifolds.

Study very stable Higgs bundles on Riemann surfaces, linking to multiplicity and mirror symmetry.

Shows CM line bundles are ample on K-stable varieties.

Classifies very stable Higgs bundles for complex groups.

Proves CM line bundle positivity for K-stable klt Fano varieties.

New approach to proving Chen-Donaldson-Sun theorem with examples.

In this paper we present a construction of stable bundles on Calabi-Yau threefolds using the method of bundle extensions. This construction applies to any given Calabi-Yau threefold with h^{1,1}>1. We give examples of stable bundles of rank 2 and 4 constructed out of pure geometric data of the given Calabi-Yau space. A…

Researchers create a stable bundle on a hyperkähler manifold's twistor space with nonstable fibers.

By the work of Hong and Tian it is known that given a holomorphic vector bundle E over a compact Kahler manifold X, the Yang-Mills flow converges away from an analytic singular set. If E is semi-stable, then the limiting metric is Hermitian-Einstein and will decompose the limiting bundle into a direct sum of stable bun…

We give a method to construct stable vector bundles whose rank divides the degree over curves of genus bigger than one. The method complements the one given by Newstead. Finally, we make some systematic remarks and observations in connection with rationality of moduli spaces of stable vector bundles.

We prove a case of the conjecture of Douglas, Reinbacher and Yau about the existence of stable vector bundles with prescribed Chern classes on a Calabi-Yau threefold. For this purpose we prove the existence of certain stable vector bundle extensions over elliptically fibered Calabi-Yau threefolds.

Stable generalized complex structures on certain surfaces are constant.

Proof that stable minimal surfaces in 3D are flat.

In this paper, we prove that the tangent bundle of the moduli space $\cSU_C(r,d)$ of stable bundles of rank $r>2$ and of fixed determinant of degree $d$ (such that $(r,d)=1$), on a smooth projective curve $C$ is always stable, in the sense of Mumford-Takemoto. This verifies a well-known conjecture, and is related to a …

In this paper we study the first eigenvalue of the Laplacian on a compact Kaehler manifold using stable bundles and balanced bases.

Unique solution found for Demailly's equation on stable bundles.

Develops deformation theory for mapping spaces related to Morse theory and Bott-Thom isomorphism.

Usually bundle gerbes are considered as objects of a 2-groupoid, whose 1-morphisms, called stable isomorphisms, are all invertible. I introduce new 1-morphisms which include stable isomorphisms, trivializations and bundle gerbe modules. They fit into the structure of a 2-category of bundle gerbes, and lead to natural d…

The purpose of this paper is to investigate canonical metrics on a semi-stable vector bundle E over a compact Kahler manifold X. It is shown that, if E is semi-stable, then Donaldson's functional is bounded from below. This implies that E admits an approximate Hermitian-Einstein structure, generalizing a classic result…

Study hermitian Yang-Mills connections on pullback bundles for holomorphic submersions.

The paper constructs stable Higgs bundles for hyperbolic metrics with singularities.

Geometric Invariant Theory applied to Kähler manifolds yields analytic models for vector bundles.

We present an explicit construction of the moduli spaces of rank 2 stable parabolic bundles of parabolic degree 0 over the Riemann sphere, corresponding to "optimum" open weight chambers of parabolic weights in the weight polytope. The complexity of the different moduli space' weight chambers is understood in terms of …

In this paper, we consider a compact Kahler manifold with extremal Kahler metric and a Mumford stable holomorphic bundle over it. We proved that, if the holomorphic vector field defining the extremal Kahler metric is liftable to the bundle and if the bundle is relatively stable with respect to the action of automorphis…

Flat holomorphic connections on stable bundles over LVMB manifolds are always flat.

Criterion for Lie algebroid connections on compact Riemann surfaces.

Constructs stable Hilbert bundles on curves using Diophantine approximation.

Characteristic classes of oriented vector bundles can be identified with cohomology classes of the disjoint union of classifying spaces BSO_n of special orthogonal groups SO_n with n=0,1,... A characteristic class is stable if it extends to a cohomology class of a homotopy colimit BSO of classifying spaces BSO_n. Simil…

Real vector bundles are determined by their Dirac indices on specific spin manifolds.

In this paper, we consider the exact triangles consisting of stable vector bundles on one-dimensional complex tori, and give a geometric interpretation of them in terms of the corresponding Fukaya category via the homological mirror symmetry.

Constructs stable bundles on K3 surfaces using monad construction.

We describe the moduli space of stable rank 2 parabolic bundles over an elliptic curve with 3 marked points.

The paper calculates curvature formulas for stable Higgs bundles.

Iterative method finds Hermitian-Einstein metrics on stable bundles.

Computes cohomology of rank 2 bundles, linking to skew Schur polynomials.

We prove that a given Calabi-Yau threefold with a stable holomorphic vector bundle can be perturbed to a solution of the Strominger system provided that the second Chern class of the vector bundle is equal to the second Chern class of the tangent bundle. If the Calabi-Yau threefold has strict SU(3) holonomy then the eq…

The moduli space of stable bundles of rank 2 and degree 1 on a Riemann surface has rational cohomology generated by the so-called universal classes. The work of Baranovsky, King-Newstead, Siebert-Tian and Zagier provided a complete set of relations between these classes, expressed in terms of a recursion in the genus. …

We study natural families of d-bar operators on the moduli space of stable parabolic vector bundles. Applying a families index theorem for hyperbolic cusp operators from our previous work, we find formulae for the Chern characters of the associated index bundles. The contributions from the cusps are explicitly expresse…

The aim of this paper is to construct the parabolic version of the Donaldson--Uhlenbeck compactification for the moduli space of parabolic stable bundles on an algenraic surface with parabolic structures along a divisor with normal crossing singularities. We prove the non--emptiness of the moduli space of parabolic sta…

New results affirmatively answer the stable converse soul question for many curved spaces.

We establish the correspondence between tame harmonic bundles and $μ_L$-stable parabolic Higgs bundles with trivial characteristic numbers. We also show the Bogomolov-Gieseker type inequality for $μ_L$-stable parabolic Higgs bundles. Then we show that any local system on a smooth quasi projective variety can be deforme…