Related papers: Nonlinear Harmonic Bundles
We establish the twisted functoriality in nonabelian Hodge theory in positive characteristic. As an application, we obtain a purely algebraic proof of the fact that the pullback of a semistable Higgs bundle with vanishing Chern classes is…
We construct spaces of coinvariants at principally polarized abelian varieties with respect to the action of an infinite-dimensional Lie algebra. We show how these spaces globalize to twisted $\mathcal{D}$-modules on moduli of principally…
Pursuing a generalization of group symmetries of modular categories to category symmetries in topological phases of matter, we study linear Hopf monads. The main goal is a generalization of extension and gauging group symmetries to category…
In symmetric Hamiltonian systems, relative equilibria usually arise in continuous families. The geometry of these families in the setting of free actions of the symmetry group is well-understood. Here we consider the question for non-free…
This is the first paper of a series. We prove an arithmetic Hodge index theorem for adelic line bundles on projective varieties over number fields. It extends the arithmetic Hodge index theorem of Faltings, Hriljac and Moriwaki on…
A particular form of non-linear $\sigma$-model, having a global gauge invariance, is studied. The detailed discussion on current algebra structures reveals the non-abelian nature of the invariance, with {\it{field dependent structure…
This paper introduces a generalization of Pontryagin duality for locally compact Hausdorff abelian groups to locally compact Hausdorff abelian group bundles.
This paper establishes some hidden connections between the theory of generalized algebraic multiplicities, the intersection index of algebraic varieties, and the notion of orientability of vector bundles. The novel approach adopted in it…
In this paper, we study the unitarizations in the spaces of holomorphic sections of equivariant holomorphic line bundles over a bounded homogeneous domain under the action of a connected algebraic group acting transitively on the domain. We…
A Mall bundle on a Hopf manifold H is a holomorphic vector bundle whose pullback to the universal cover of H is trivial. We define resonant and non-resonant Mall bundles, generalizing the notion of the resonance in ODE, and prove that a…
We describe work on solutions of certain non-divergence type and therefore non-variational elliptic and parabolic systems on manifolds. These systems include Hermitian and affine harmonics which should become useful tools for studying…
We introduce a certain differential graded bialgebra, neither commutative nor cocommutative, that governs perturbations of a differential on complexes supplied with an abstract Hodge decomposition. This leads to a conceptual treatment of…
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…
We establish the generalized canonical bundle formula for generalized lc-trivial fibrations with irrational coefficients over non-compact bases in the complex analytic setting, and we show that the discriminant b-divisor and moduli…
We study rank $1$ flat bundles over solvmanifolds whose cohomologies are non-trivial. By using Hodge theoretical properties for all topologically trivial rank $1$ flat bundles, we represent the structure theorem of K\"ahler solvmanifolds as…
We propose an approach to study logarithmic sheaves T(-log A) associated with a hyperplane arrangements A on the projective space, based on projective duality, direct image functors and vector bundles methods. We focus on freeness of line…
We show a relationship between Chern-Simons 1- and 3-forms and harmonic forms on a principal bundle. Doing so requires one to consider an adiabatic limit. For the 3-form case, assume that G is simple and the corresponding Chern-Weil 4-form…
We define the notion of a holomorphic bundle on the noncommutative toric orbifold $T_{\theta}/G$ associated with an action of a finite cyclic group $G$ on an irrational rotation algebra. We prove that the category of such holomorphic…
Higher bundles are homotopy coherent generalisations of classical fibre bundles. They appear in numerous contexts in geometry, topology and physics. In particular, higher principal bundles provide the geometric framework for higher-group…
In this paper we introduce a generalisation of the notion of holonomy for connections over a bundle map on a principal fibre bundle. We prove that, as in the standard theory on principal connections, the holonomy groups are Lie subgroups of…