相关论文: Hitchin systems on ll- curves
We study effective versions of unlikely intersections of images of torsion points of elliptic curves on the projective line.
We present a new unified theory of critical finite-size scaling for lattice statistical mechanical models with periodic boundary conditions above the upper critical dimension. Our theory is based on recent mathematically rigorous results…
This is a survey on recent results on counting of curves over finite fields. It reviews various results on the maximum number of points on a curve of genus g over a finite field of cardinality q, but the main emphasis is on results on the…
We study the existence of Artin-Schreier curves with large $ a$-number. We also give bounds on the $a$-number of trigonal curves of genus $5$ in small characteristic.
This paper concerns the number of lattice points in a circle.
We construct curves with many points over finite fields using the class group
Given a real curve, we study special linear systems called "very special" for which the dimension does not satisfy a Clifford type inequality. We classify all these very special linear systems when the gonality of the curve is small.
Some recent developments in the theory of quantum spin systems are reviewed.
We give new bounds for the number of integral points on elliptic curves. The method may be said to interpolate between approaches via diophantine techniques ([BP], [HBR]) and methods based on quasiorthogonality in the Mordell-Weil lattice…
We establish sharp lower and upper bounds for the number of integral points near dilations of a space curve with nowhere vanishing torsion.
We discuss critical elliptic systems in potential form. We prove existence, multiplicity, and compactness of solutions.
We discuss integrable discretizations of 3-dimensional cyclic systems, that is, orthogonal coordinate systems with one family of circular coordinate lines. In particular, the underlying circle congruences are investigated in detail, and…
We formulate a refined theory of linear systems, using the methods of a previous paper, "A Theory of Branches for Algebraic Curves", and use it to give a geometric interpretation of the genus of an algebraic curve. Using principles of…
Knizhnik-Zamolodchikov-Bernard (KZB) equation on an elliptic curve with a marked point is derived by the classical Hamiltonian reduction and further quantization. We consider classical Hamiltonian systems on cotangent bundle to the loop…
We study topologically trivial $G$-Higgs bundles over an elliptic curve $X$ when the structure group $G$ is a connected real form of a complex semisimple Lie group $G^{\mathbb{C}}$. We achieve a description of their (reduced) moduli space,…
In this paper, we almost completely solve the existence of an almost resolvable cycle system with odd cycle length. We also use almost resolvable cycle systems as well as other combinatorial structures to give some new solutions to the…
Given a parametrisation of an elliptic curve over Q by a Shimura curve, we show that the images of almost all Heegner points are of infinite order. For parametrisations of elliptic curves by modular curves this was proven earlier by Nekovar…
We investigate space curves with large cohomology. To this end we introduce curves of subextremal type. This class includes all subextremal curves. Based on geometric and numerical characterizations of curves of subextremal type, we show…
In this study, we define a new type of direction curves in the Euclidean 3-space such as osculating-direction curve. We give the characterizations for these curves. Moreover, we obtain the relationships between osculating direction curves…
The supersymmetric theory of (color)superconductivity is investigated.