Related papers: On SUSY curves
Topologically, a compact Riemann surface $X$ of genus $g$ is a $g$-holed torus (a sphere with $g$ handles). This paper is an introduction to the theory of compact Riemann surfaces and algebraic curves. It presents the basic ideas and…
SU(2) flat connection on 2D Riemann surface is shown to relate to the generalized twisted geometry in 3D space with cosmological constant. Various flat connection quantities on Riemann surface are mapped to the geometrical quantities in…
We sketch the development of effective theories for SU(2) and SU(3) Yang-Mills thermodynamics. The most important results are quoted and some implications for particle physics and cosmology are discussed.
Different ways to incorporate two-dimensional systems, which are not amenable to separation of variables, into the framework of Supersymmetrical Quantum Mechanics (SUSY QM) are analyzed. In particular, the direct generalization of…
In this paper we relate some classical normal forms for complex elliptic curves in terms of 4-point sets in the Riemann sphere. Our main result is an alternative proof that every elliptic curve is isomorphic as a Riemann surface to one in…
In this paper, almost product-like Riemannian manifolds are investigated. Basic properties on tangential hypersurfaces of almost product-like Riemannian manifolds are obtained. Some examples of tangential hypersurfaces are presented. Some…
We establish a defect relation of holomorphic curves from a general open Riemann surface into a normal complex projective variety, with Zariski-dense image intersecting effective Cartier divisors.
We present an overview of the differential geometry of curves and surfaces using examples from soft matter as illustrations. The presentation requires a background only in vector calculus and is otherwise self-contained.
We present a survey of some results and questions related to the notion of scalar curvature in the setting of symplectic supermanifolds.
We derive curvature estimates for minimal submanifolds in Euclidean space for arbitrary dimension and codimension via Gauss map. Thus, Schoen-Simon-Yau's results and Ecker-Huisken's results are generalized to higher codimension. In this way…
Gorsky et al. presented an explicit construction of Whitham deformations of the Seiberg-Witten curve for the $SU(N+1)$ $\calN = 2$ SUSY Yang-Mills theory. We extend their result to all classical gauge groups and some other cases such as the…
A theorem of Wiegerinck asserts that the Bergman space of an open subset of the complex numbers is either infinite-dimensional or trivial. Recently, this has been generalized to holomorphic vector bundles over the projective line by the…
We give bounds for exponential sums over curves defined over Galois rings. We first define summation subsets as the images of lifts of points from affine opens of the reduced curve, and we give bounds for the degrees of their coordinate…
Recent development in numerical simulations of supersymmetric Yang-Mills (SYM) theories on the lattice is reviewed.
In this note we clarify that the Rcci flow can be used to give an independent proof of the uniformization theorem of Riemann surfaces.
We derive presentation and relations for a group of compact Riemann surface that is given as branched cover of the sphere. In the case that one of the permutations is of full cycle of the form $(1...n)$ we derive a straightforward process…
By modifying Cole's example, we construct explicit Riemann surfaces with large bounds on corona solutions in an elementary way.
This paper is the third in a series dedicated to the fundamentals of sub-Riemannian geometry and its implications in Lie groups theory: "Sub-Riemannian geometry and Lie groups. Part I", math.MG/0210189, available at…
We derive the low-energy effective theory on the BPS domain wall in 4D N=1 global SUSY theories in terms of the 3D superfields. Our derivation makes the preserved SUSY by the wall manifest and the procedure for integrating out the massive…
The goal of this paper is to develop some aspects of the deformation theory of piecewise flat structures on surfaces and use this theory to construct new geometric structures on the moduli space of Riemann surfaces.