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Noncommutative Tate curves
ate curves UHF-algebras
2011/1/17
It is proved, that the homology group of the Tate curve is the Pontryagin dual to the K-theory of the UHF-algebras.
Brauer group of moduli of principal bundles over a curve
Brauer group principal bundle moduli space curve
2011/2/24
Let G be a semisimple linear algebraic group over the field C, and let C be an irreducible smooth complex projective curve of genus at least three. We compute the Brauer group of the smooth locus of t...
We give an informal survey, emphasizing examples and open problems, of two interconnected research programs in moduli of curves: the systematic classi cation of modular compacti cations of Mg;n, and t...
Universal Hyperbolic Geometry II: A pictorial overview
Universal Hyperbolic Geometry II pictorial overview
2011/1/18
This article provides a simple pictorial introduction to universal hyperbolic geometry. We explain how to understand the subject using only elementary projective geometry, augmented by a distinguished...
The second pinching theorem for hypersurfaces with constant mean curvature in a sphere
Hypersurfaces with constant mean curvature Rigidity Scalar curvature Clifford torus
2011/1/20
We generalize the second pinching theorem for minimal hypersurfaces in a sphere due to Peng-Terng, Wei-Xu, Zhang, and Ding-Xin to the case of hypersurfaces with small constant mean curvature. Let Mn b...
On the Convex Hull of the Points on Modular Hyperbolas
congruence modular hyperbola integral polygon convex hull
2011/1/19
Given integers a and m ≥ 2, let Ha(m) be the following set of integral points Ha(m) = {(x, y) : xy ≡ a (mod m), 1 ≤ x, y ≤ m − 1} We improve several previously known upper bounds on va(m), the n...
Uniqueness of the Foliation of Constant Mean Curvature Spheres in Asymptotically Flat 3-Manifolds
Uniqueness Foliation of Constant Mean Curvature Spheres Asymptotically Flat 3-Manifolds
2011/2/21
In this paper I study the constant mean curvature surface in asymp-totically flat 3-manifolds with general asymptotics. Under some weak condition, I prove that outside some compact set in the asymptot...
On the rational Picard group of the moduli space of curves
rational Picard group moduli space of curves
2011/2/25
We speculate about an algebro-geometric proof of Harer’s theorem on the rational Picard group of the moduli space of smooth complex curves. In particular, we refine the approach of Diaz and Edidin in-...
Two families of maximal curves which are not Galois subcovers of the Hermitian curve
maximal curves generalized GK curves Galois coverings
2011/1/20
We show that the generalized Giulietti-Korchm´aros curve and the maximal curve with equation x q2 − x = y (qn+1)/(q+1) defined over F q2n, for n 3 odd and q 3, are not Galois subcovers...
Compact Mean Convex Hypersurfaces and the Fundamental Group of Manifolds with Nonnegative Ricci Curvature
Compact Mean Convex Hypersurfaces Fundamental Group of Manifolds Nonnegative Ricci Curvature
2011/1/19
We show that the existence of an embedded compact, boundaryless hypersurface S of strictly
positive mean curvature in a noncompact, connected, complete Riemannian n-manifold N of non-
negative Ricci...
Giulietti and Korchm´aros presented new curves with the maximal number of points over a field of size q6. Garcia, G¨uneri, and Stichtenoth extended the construction to curves that are maximal ov...
Uniqueness for a hyperbolic inverse problem with angular control on the coefficients
Inverse Problems Wave Equation
2011/2/22
Suppose qi(x), i = 1; 2 are smooth functions on R3 and Ui(x; t) the solutions of the initial
value problem @2 t Ui Ui qi(x)Ui = (x; t); (x; t) 2 R3 R Ui(x; t) = 0; for t < 0...
For a domain D ⊂ Cn we construct a continuous fo-liation of D into one real dimensional curves such that any func-tion f ∈ C1(D) which can be extended holomorphically into some
neighborhood of ...
A complex surface of general type with $p_g=0$, $K^2=2$ and $H_1=\mathbb{Z}/4\mathbb{Z}$
complex surface of general type $p_g=0$, $K^2=2$ $H_1=\mathbb{Z}/4\mathbb{Z}$
2011/2/28
One of the greatest difficulties encountered by all in their first proof intensive class is
subtly assuming an unproven fact in a proof. The purpose of this note is to describe a specific instance wh...
Counting lattice points in compactified moduli spaces of curves
Counting lattice points compactified moduli spaces of curves
2011/3/1
We define and count lattice points in the moduli spaceMg,n of stable genus g curves with n labeled points.