Divisor

About: Divisor is a research topic. Over the lifetime, 2462 publications have been published within this topic receiving 21394 citations. The topic is also known as: factor & submultiple.

Conical Kahler-Einstein metric revisited

Abstract: In this paper we introduce the "interpolation-degneration" strategy to study Kahler-Einstein metrics on a smooth Fano manifold with cone singularities along a smooth divisor that is proportional to the anti-canonical divisor. By "interpolation" we show the angles in $(0, 2\pi]$ that admit a conical Kahler-Einstein metric form an interval; and by "degeneration" we figure out the boundary of the interval. As a first application, we show that there exists a Kahler-Einstein metric on $P^2$ with cone singularity along a smooth conic (degree 2) curve if and only if the angle is in $(\pi/2, 2\pi]$. When the angle is $2\pi/3$ this proves the existence of a Sasaki-Einstein metric on the link of a three dimensional $A_2$ singularity, and thus answers a problem posed by Gauntlett-Martelli-Sparks-Yau. As a second application we prove a version of Donaldson's conjecture about conical Kahler-Einstein metrics in the toric case using Song-Wang's recent existence result of toric invariant conical Kahler-Einstein metrics.

The cone of type A, level one conformal blocks divisors

Abstract: We prove that the type A, level one, conformal blocks divisors on $\bar{M}_{0,n}$ span a finitely generated, full-dimensional subcone of the nef cone. Each such divisor induces a morphism from $\bar{M}_{0,n}$, and we identify its image as a GIT quotient parameterizing configurations of points supported on a flat limit of Veronese curves. We show how scaling GIT linearizations gives geometric meaning to certain identities among conformal blocks divisor classes. This also gives modular interpretations, in the form of GIT constructions, to the images of the hyperelliptic and cyclic trigonal loci in $\bar{M}_{g}$ under an extended Torelli map.

Decomposition Attack for the Jacobian of a Hyperelliptic Curve over an Extension Field

Abstract: We propose some kind of new attack which gives the solution of the discrete logarithm problem for the Jacobian of a curve defined over an extension field \(\mathbb{F}_{q^{n}}\), considering the set of the union of factor basis and large primes B 0 given by points of the curve whose x-coordinates lie in \(\mathbb{F}_q\). In this attack, an element of the divisor group which is written by a sum of some elements of factor basis and large primes is called (potentially) decomposed and the set of the factors that appear in the sum, is called decomposed factors. So, it will be called decomposition attack. In order to analyze the running of the decomposition attack, a test for the (potential) decomposedness and the computation of the decomposed factors are needed. Here, we show that the test to determine if an element of the Jacobian (i.e., reduced divisor) is written by an ng sum of the elements of the decomposed factors and the computation of decomposed factors are reduced to the problem of solving some multivariable polynomial system of equations by using the Riemann-Roch theorem. In particular, in the case of hyperelliptic curves of genus g, we construct a concrete system of equations, which satisfies these properties and consists of (n 2 − n)g quadratic equations. Moreover, in the case of (g,n) = (1,3),(2,2) and (3,2), we give examples of the concrete computation of the decomposed factors by using the computer algebra system Magma.

Gauging 1-form center symmetries in simple SU(N) gauge theories

Abstract: Consequences of gauging exact $$ {\mathbb{Z}}_k^C $$ center symmetries in several simple SU(N) gauge theories, where k is a divisor of N, are investigated. Models discussed include: the SU(N) gauge theory with Nf copies of Weyl fermions in self-adjoint single-column antisymmetric representation, the well-discussed adjoint QCD, QCD-like theories in which the quarks are in a two-index representation of SU(N), and a chiral SU(N) theory with fermions in the symmetric as well as in anti-antisymmetric representations but without fundamentals. Mixed 't Hooft anomalies between the 1-form $$ {\mathbb{Z}}_k^C $$ symmetry and some 0- form (standard) discrete symmetry provide us with useful information about the infrared dynamics of the system. In some cases they give decisive indication to select only few possiblities for the infrared phase of the theory.