Related papers: Hitchin systems on ll- curves

We determine the crossing number of polynomial size curve systems on standard surfaces, in terms of the genus, up to high precision.

A great number of works is devoted to qualitative investigation of Hamiltonian systems. One of tools of such investigation is the method of skew-symmetric differential forms. In present work, under investigation Hamiltonian systems in…

A system of plane curves defined by prescribing n points of multiplicity m in general position is regular if n > (2m)^2. The proof uses computation of limits of linear systems acquiring fixed divisors, an interesting problem in itself.

We discuss geometrical aspects of different dualities in the integrable systems of the Hitchin type and its various generalizations. It is shown that T duality known in the string theory context is related to the separation of variables…

In this paper we calculate the curvature of the Hitchin connection. We further show that a slight (possibly trivial) modification of the Hitchin connection has curvature equal to an explict given multiple of the Weil-Petersen symplectic…

A typical solution of an integrable system is described in terms of a holomorphic curve and a line bundle over it. The curve provides the action variables while the time evolution is a linear flow on the curve's Jacobian. Even though the…

We study the curl-div-system with variable coefficients and a nonlocal homogenisation problem associated with it. Using, in part refining, techniques from nonlocal $H$-convergence for closed Hilbert complexes, we define the appropriate…

A linear system of plane curves satisfying multiplicity conditions at points in general position is called special if the dimension is larger than the expected dimension. A (-1) curve is an irreducible curve with self intersection -1 and…

The paper reviews various arithmetic analogues of Hamiltonian systems and presents some new facts suggesting ways to relate/unify these examples.

We investigate the Hilbert scheme of points on curves with n-fold singularities, that is curves that look locally around their singular points as the axis in an affine space. We describe the structure and number of its irreducible…

Here Lipschitz conditions are used as a primary tool, for studying curves in metric spaces in particular.

We give an efficient algorithm to compute equations of twists of hyperelliptic curves of arbitrary genus over any separable field (of characteristic different from 2), and we explicitly describe some interesting examples.

We describe non-autonomous Hamiltonian systems coming from the Hitchin integrable systems. The Hitchin integrals of motion depend on the W-structures of the basic curve. The parameters of the W-structures play the role of times. In…

This talk gives an introduction into the subject of Seiberg-Witten curves and their relation to integrable systems. We discuss some motivations and origins of this relation and consider explicit construction of various families of…

We consider linear systems on toric varieties of any dimension, with invariant base points, giving a characterization of special linear systems. We then make a new conjecture for linear systems on rational surfaces.

We study existence of Hamilton cycles in connected Cayley graphs on generalized dihedral groups

We give a stack-theoretic proof for some results on families of hyperelliptic curves.

A family of polynomials linked to the set of the deltoid tangents and its associated algebraic hypersurfaces has been presented in recent years. In this paper we study some related maximising and free plane curves. We also analyse the…

We will generalize the Treibich-Verdier theory about elliptic solitons to a Hitchin system by constructing a particular ruled surface and we will propose a generalization of a tangency condition associated with elliptic solitons to a…

In this article we define new flows on the Hitchin components for PGL(V). Special examples of these flows are associated to simple closed curves on the surface and give generalized twist flows. Other examples, so called eruption flows, are…