相关论文: Nonlinear Hodge equations in vector bundles

We construct nonlinear representations of the Poincare, Galilei, and conformal algebras on a set of the vector-functions $\Psi =(\vec E, \vec H)$. A nonlinear complex equation of Euler type for the electromagnetic field is proposed. The…

The appearance of the Bethe Ansatz equation for the Nonlinear Schr\"{o}dinger equation in the equivariant integration over the moduli space of Higgs bundles is revisited. We argue that the wave functions of the corresponding two-dimensional…

We investigate solutions to a nonlinear integral equation which has a central role in implementing the non-Abelian Gauss's Law and in constructing gauge-invariant quark and gluon fields. Here we concern ourselves with solutions to this same…

The objective of this work is to establish a systematic study of boundary value problems within the framework of differential forms and variable exponent spaces. Specifically, we investigate the Hodge Laplacian and related first order…

In this paper, we study nonlinear differential equations satisfied by the generating function of Boole numbers. In addition, we derive some explicit and new interesting identities involving Boole numbers and higher-order numbers arising…

We show how quiver representations and their invariant theory natu- rally arise in the study of some moduli spaces parametrizing bundles dened on an algebraic curve, and how they lead to ne results regarding the geometry of these spaces.

This is an expository article on the theory of algebraic stacks. After introducing the general theory, we concentrate in the example of the moduli stack of vector budles, giving a detailed comparison with the moduli scheme obtained via…

We compute the cohomological invariants of $\mathcal{H}_g$, the moduli stack of smooth hyperelliptic curves, for every odd $g$.

We study an algebraic inequality for nilpotent matrices and show some interesting geometric applications: (i) obtaining topological information for nilpotent polystable Higgs bundles over a compact Riemann surface; (ii) obtaining a sharp…

The equations of motion of a mechanical system subjected to nonholonomic linear constraints can be formulated in terms of a linear almost Poisson structure in a vector bundle. We study the existence of invariant measures for the system in…

We review some selected aspects of the construction of gauge invariant operators in field theories on non-commutative spaces and their relation to the energy momentum tensor as well as to the non-commutative loop equations.

In this paper, we study how certain vector bundles on an elliptic surface are changed under logarithmic transformations.

In this paper, we introduce some new ideas to study Schrodinger equations in RN with power-type nonlinearities.

We present a geometric interpretation of the integration-by-parts formula on an arbitrary vector bundle. As an application we give a new geometric formulation of higher-order variational calculus.

When $k<n$, we study the coherent systems that come from a BGN extension in which the quotient bundle is strictly semistable. In this case we describe a stratification of the moduli space of coherent systems. We also describe the strata as…

Based on work of R. Lazarsfeld and M. Popa, we use the derivative complex associated to the bundle of the holomorphic p-forms to provide inequalities for all the Hodge numbers of a special class of irregular compact Kaehler manifolds. For…

We compute the behaviour of Hodge data under additive middle convolution for irreducible variations of polarized complex Hodge structures on punctured complex affine lines.

Differential calculi are obtained for quantum homogeneous spaces by extending Woronowicz' approach to the present context. Representation theoretical properties of the differential calculi are investigated. Connections on quantum…

Quantum theory of the gauge models in the causal approach leads to some cohomology problems. We investigate these problems in detail.

We describe methods for calculation of polytopes of quasiadjunction for plane curve singularities which are invariants giving a Hodge theoretical refinement of the zero sets of multivariable Alexander polynomials. In particular we identify…