ﻻ يوجد ملخص باللغة العربية
We formulate a correspondence between SU(2) monopole chains and ``spectral data, consisting of curves in $mathbb{CP}^1timesmathbb{CP}^1$ equipped with parabolic line bundles. This is the analogue for monopole chains of Donaldsons association of monopoles with rational maps. The construction is based on the Nahm transform, which relates monopole chains to Higgs bundles on the cylinder. As an application, we classify charge $k$ monopole chains which are invariant under actions of $mathbb{Z}_{2k}$. We present images of these symmetric monopole chains that were constructed using a numerical Nahm transform.
In this paper we count the number of isomorphism classes of geometrically indecomposable quasi-parabolic structures of a given type on a given vector bundle on the projective line over a finite field. We give a conjectural cohomological interpretatio
By studying the Higgs bundle equations with the gauge group replaced by the group of symplectic diffeomorphisms of the 2-sphere we encounter the notion of a folded hyperkaehler 4-manifold and conjecture the existence of a family of such metrics param
This is a sequel to Kodaira-Saito vanishing via Higgs bundles in positive characteristic (arXiv:1611.09880). However, unlike the previous paper, all the arguments here are in characteristic zero. The main result is a Kodaira vanishing theorem for sem
In this paper we study the geometry of the moduli space of (non-strongly) parabolic Higgs bundles over a Riemann surface with marked points. We show that this space possesses a Poisson structure, extending the one on the dual of an Atiyah algebroid o
We prove a Torelli theorem for the moduli space of semistable parabolic Higgs bundles over a smooth complex projective algebraic curve under the assumption that the parabolic weight system is generic. When the genus is at least two, using this result