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About a moduli space of elliptic curves and the Golay code G_{24}
moduli space elliptic curves Golay code G_{24}
2011/1/20
We investigate algebraic structures related to triangle decompositions of a moduli space of complex tori given by the Veech curve T. We show that these structures produce the binary error correcting ...
On a General Linear Nonlocal Curvature Flow of Convex Plane Curves
General Linear Nonlocal Curvature Flow Convex Plane Curves
2011/1/17
Motivated by Pan-Yang [PY] and Ma-Cheng [MC], we study a general linear nonlocal cur-vature flow for convex closed plane curves and discuss the short time existence and asymptotic
convergence behavio...
We study the inertia stack of [M_{0,n}/S_n], the quotient stack of the moduli stack of smooth genus 0 curves with n marked points via the action of the symmetric group S_n. Then we see how from this ...
Semi-stable vector bundles on elliptic curves and the associative Yang-Baxter equation
elliptic curves the associative Yang-Baxter equation
2010/11/23
In this paper we study unitary solutions of the associative Yang--Baxter equation (AYBE) with spectral parameters. We show that to each point $\tau$ from the upper half-plane and an invertible $n \tim...
Let $M$ be the moduli space of rank $2$ stable bundles with fixed determinant of degree $1$ on a smooth projective curve $C$ of genus $g\ge 2$. When $C$ is generic, we show that any elliptic curve on...
Mori's program for the moduli space of pointed stable rational curves
Mori's program the moduli space
2010/11/22
We prove that, assuming the F-conjecture, the log canonical model of the pair $(\bar{M}_{0,n}, \sum a_i \psi_i)$ is the Hassett's moduli space of weighted pointed stable rational curves without any mo...
Birkhoff strata of the Grassmannian Gr$\mathrm{^{(2)}}$: Algebraic curves
Birkhoff strata the Grassmannian
2010/11/23
Algebraic varieties and curves arising in Birkhoff strata of the Sato Grassmannian Gr${^{(2)}}$ are studied. It is shown that the big cell $\Sigma_0$ contains the tower of families of the normal rati...
We study the stable pairs theory of local curves in 3-folds with descendent insertions. The rationality of the partition function of descendent invariants is established for the full local curve geom...
Irreducibility of the space of cyclic covers of algebraic curves of fixed numerical type and the irreducible components of $Sing (\bar{\mathfrak M_g})$
space algebraic curves numerical type irreducible components
2010/11/8
We prove irreducibility for the space of cyclic covers of fixed numerical type between smooth projective curves, and also for the space of cyclic covers of prime order and of fixed numerical-combinato...
Let $C$ be a smooth (irreducible) curve of degree $d$ in $\mathbb{P}^{2}$. Let $\mathbb{P}^{2} \hookrightarrow \mathbb{P}^{5}$ be the Veronese embedding and let $\mathcal{I}_{C}$ denote the homogeneo...
The complex AGM, periods of elliptic curves over C and complex elliptic logarithms
The complex AGM elliptic curves complex elliptic logarithms
2010/11/9
We present a method for computing period lattices and elliptic logarithms for elliptic curves defined over C, using the complex Arithmetic-Geometric Mean (AGM) first studied by Gauss. Earlier authors ...
Density of rational points on elliptic curves and small transcendence degree
rational points elliptic curves
2010/11/19
In this paper we pursue two goals: (I) We show how Weil restrictions to real subfields can be fruitfully applied to improve transcendence results. (II) We elaborate (I) in the context of algebraic in...
Lectures on Holomorphic Curves in Symplectic and Contact Geometry
Holomorphic Curves Symplectic Contact Geometry
2010/11/12
This is a set of expository lecture notes created originally for a graduate course on holomorphic curves taught at ETH Zurich and the Humboldt University Berlin in 2009/2010. The notes are still incom...
Suppose a smooth planar curve $\gamma$ is $2\pi$-periodic in the $x$ direction and the length of one period is $\ell$. It is shown that if $\gamma$ self-intersects, then it has a segment of length $\...
Analytic continuation of functions along parallel algebraic curves
Analytic continuation functions along parallel algebraic curves
2010/11/11
In this work we study a problem about analytic continuation along parallel algebraic curves