相关论文: Hitchin systems on ll- curves

Higher diameters of Cayley digraphs are defined and studied.

We investigate the interplay between linear systems on curves and graphs in the context of specialization of divisors on an arithmetic surface. We also provide some applications of our results to graph theory, arithmetic geometry, and…

We consider smooth surfaces $S \subset \Pq$ containing a plane curve $P$ and prove some general result concerning the linear system $|H-P|$. We then look at regular surfaces lying on hypersurfaces of degree $s$ having a plane of…

We apply classical invariant theory of binary forms to explicitly characterize isomorphism classes of hyperelliptic curves of small genus and, conversely, propose algorithms for reconstructing hyperelliptic models from given invariants. We…

In this paper, we consider a generalization of the theory of Higgs bundles over a smooth complex projective curve in which the twisting of the Higgs field by the canonical bundle of the curve is replaced by a rank 2 vector bundle. We define…

We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types…

We exhibit a precise connection between N\'eron--Tate heights on smooth curves and biextension heights of limit mixed Hodge structures associated to smoothing deformations of singular quotient curves. Our approach suggests a new way to…

Let $H$ be the Hilbert scheme of curves in complex projective $3$-space, with $d\geq 3$ and genus $g \leq (d-2)^2/4$. A complete, explicit description of the cone of curves and the ample cone of $H$ is given. From this, partial results on…

We consider the Li\'enard equation and we give a sufficient condition to ensure existence and uniqueness of limit cycles. We compare our result with some other existing ones and we give some applications.

For linear infinite systems the approximate controllability problem by control constraints is considered. Controllability conditions represented via system parameters are obtained. Partial differential control systems and control systems…

Let S be the boundary of a handlebody M. We prove that the set of curves in S that are boundaries of disks in M, considered as a subset of the complex of curves of S, is quasi-convex.

In this paper we investigate the properties of the real and complex projective structures associated to Hitchin and quasi-Hitchin representations that were originally constructed using Guichard-Wienhard's theory of domains of discontinuity.…

Higher rank Brill-Noether theory is completely known for curves of genus $\leq 3$. In this paper, we investigate the theory for curves of genus 4. Some of our results apply to curves of arbitrary genus.

We study analysis over infinite dimensional manifolds consisted by sequences of almost Kaehler manifolds. We develop moduli theory of pseudo holomorphic curves into such spaces with high symmetry. Many mechanisms of the standard moduli…

The aim of this paper is two-fold. First, we define symplectic maps between Hitchin systems related to holomorphic bundles of different degrees. We call these maps the Symplectic Hecke Correspondence (SHC) of the corresponding Higgs…

Some new kinds of special curves called $\overset{\_}{\xi}$-helix, $\overset{% \_}{\xi}_{1}$-helix, $\overset{\_}{\mu}$-helix, $\overset{\_}{\nu}$-helix and $W_{k}$-Darboux helices $(k\in \left\{ {n,r,o}\right\} )$ in the Myller…

We study two-dimensional systems with boundary curves described by power laws. Using conformal mappings we obtain the correlations at the bulk critical point. Three different classes of behaviour are found and explained by scaling arguments…

We study the length of short cycles on uniformly random metric maps (also known as ribbon graphs) of large genus using a Teichm\"uller theory approach. We establish that, as the genus tends to infinity, the length spectrum converges to a…

Final version, to appear in Mathematical Research Letters.

We introduce one dimensional sets to help describe and constrain the integral curves of an $n$ dimensional dynamical system. These curves provide more information about the system than the zero-dimensional sets (fixed points) do. In fact,…