My main project to date ([3]) is concerned with certain moduli spaces of Higgs bundles and isomorphisms between them, which arise from natural operations on the bundles. Conventionally1, a Higgs bundle is a pair (V, φ) on a Riemann surface X. Here V is a vector bundle (algebraic) and φ is a linear map V → ΩX⊗V called the Higgs field. Why consider such pairs? If nothing else, maybe a Higgs bundl...

The Lie derivation of multivector fields along multivector fields has been introduced by Schouten (see cite{Sc, S}), and studdied for example in cite{M} and cite{I}. In the present paper we define the Lie derivation of differential forms along multivector fields, and we extend this concept to covariant derivation on tangent bundles and vector bundles, and find natural relations between them and...

Given a vector bundle E on a smooth projective variety X, we can define subschemes of the Kontsevich moduli space of genus-zero stable maps M0,0(X, β) parameterizing maps f : P1 → X such that the Grothendieck decomposition of f∗E has a specified splitting type. In this paper, using a “compactification” of this locus, we define Gromov-Witten invariants of jumping curves associated to the bundle ...

DIP-VBTV: A Color Image Restoration Model Combining a Deep Prior and Vector Bundle Total Variation

INTRODUCTION THE existence of a non-zero vector field on a differentiable manifold M yields geometric and algebraic information about M. For example, (I) A non-zero vector field exists on M if and only if the tangent bundle of M splits off a trivial bundle. (2) The kth Stiefel-Whitney class W,(M) of M is the primary obstruction to obtaining (n -k + I) linearly independent non-zero vector fields...

A subbundle of variable dimension inside the tangent bundle of a smooth manifold is called a smooth distribution if it is the pointwise span of a family of smooth vector fields. We prove that all such distributions are finitely generated, meaning that the family may be taken to be a finite collection. Further, we show that the space of smooth sections of such distributions need not be finitely ...

The above remarks set up a basic link between non degenerate multidimensional matrices of boundary format and vector bundles on a product of projective spaces. In the particular case p = 2 the (dual) vector bundle SA lives on the projective space P , n = k2, and is a Steiner bundle as defined in [DK]. We can keep to SA the name Steiner also for p ≥ 3. The action of of SL(V0)×. . .×SL(Vp) onA tr...

Given a vector bundle on P1 bundle, the base is stratified by degeneracy loci measuring splitting type of restricted to each fiber. The classes these in Chow ring or cohomology are natural invariants characterizing degenerations bundle. When occur expected codimension, we find their classes. This yields universal formulas for terms naturally arising bundles base. existence applied prove non-emp...

Based on the usual Fedosov construction of star products for a symplectic manifold M we give a simple geometric construction of a bimodule deformation for the sections of a vector bundle over M starting with a symplectic connection on M and a connection for E. In the case of a line bundle this gives a Morita equivalence bimodule where the relation between the characteristic classes of the Morit...

Building on Fujita-Griffiths method of computing metrics on Hodge bundles, we show that the direct image of an adjoint semi-ample line bundle by a projective submersion has a continuous metric with Griffiths semi-positive curvature. This shows that for every holomorphic semi-ample vector bundle E on a complex manifold, and every positive integer k, the vector bundle SE ⊗ detE has a continuous m...