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Hall algebras of curves, commuting varieties and Langlands duality
Hall algebras of curves commuting varieties Langlands duality
2010/11/29
We construct an isomorphism between the (universal) spherical Hall algebra of a smooth projective curve of genus g and a convolution algebra in the (equivariant) K-theory of the genus g commuting vari...
Holomorphic Cartan geometries, Calabi--Yau manifolds and rational curves
Cartan geometry holomorphic connection Calabi–Yau manifold rational curve
2010/12/14
We prove that if a Calabi–Yau manifold M admits a holomorphic Cartan geometry, then M is covered by a complex torus. This is done by establishing the Bogomolov inequality for semistable sheaves on com...
The universal theta divisor over the moduli space of curves
universal theta divisor moduli space of curves
2010/11/26
The universal theta divisor over the moduli space Ag of principally polarized abelian varieties of dimension g, is the divisor g inside the universal abelian variety Xg over Ag.
Topological recursion for the Poincare polynomial of the combinatorial moduli space of curves
Topological recursion Poincare polynomial combinatorial moduli space of curves
2010/12/3
We show that the Poincare polynomial associated with the orbifold cell decomposition of the moduli space of smooth algebraic curves with distinct marked points satis es a topological
recursion formu...
In [BL94] Beauville and Laszlo give an interpretation of the affine Grassmannian for Gln over a field k as a moduli space of, loosely speak-ing, vector bundles over a projective curve together with a ...
Evolution of plane curves with a curvature adjusted tangential velocity
curvature driven flow of plane curves curvature adjusted tangential velocity
2010/12/6
We study evolution of closed embedded plane curves with the normal veloc-ity depending on the curvature, the orientation and position of a curve. We propose a new method of tangential redistribution o...
The Kontsevich constants for the volume of the moduli of curves and topological recursion
Kontsevich constants volume of the moduli of curves topological recursion
2010/12/3
We give an Eynard-Orantin type topological recursion formula for the canonical Euclidean
volume of the combinatorial moduli space of pointed smooth algebraic curves. The recursion
comes from the edg...
Nontrivial algebraic cycles in the Jacobian varieties of some quotients of Fermat curves
Nontrivial algebraic cycles Jacobian varieties of some quotients of Fermat curves
2010/11/26
We obtain the trace map images of the values of certain harmonic vol-umes for some quotients of Fermat curves. These provide the algorithm showing that the algebraic cycles called by k-th Ceresa cycle...
We give some results on quadratic normality of reducible curves canonically embedded and partially extend this study to their projective normality.
We introduce a notion of local tropical variety which is a straightforward extension of tropism introduced by Maurer, and prove a variant of the fundamental theorem of tropical algebraic geometry in s...
On isolated smooth curves of low genera in Calabi-Yau complete intersection threefolds
isolated curves deformations Hilbert schemes Calabi-Yau threefolds
2010/12/10
Building on results of Clemens and Kley, we find criteria for a continuous family of curves in a nodal K-trivial threefold Y0 to deform to a scheme of finitely many smooth isolated curves in a general...
Polynomial estimates, exponential curves and Diophantine approximation
Polynomial estimates exponential curves Diophantine approximation
2010/12/10
Let ∈ (0, 1) \ Q and K = {(ez, e z) : |z| ≤ 1} ⊂ C2. If P is a polynomial of degree n in C2, normalized by kPkK = 1, we obtain sharp estimates for kPk2 in terms of n, where 2 is the closed u...
Vector bundles on elliptic curves and factors of automorphy
elliptic curves factors of automorphy
2010/12/8
We translate the Atiyah’s results on classification of vector bundles on elliptic curves to the language of factors of automorphy.
In this paper, we develop the theory of flashes of an algebraic curve. We show that the theory is birationally invariant in a sense which we will make more precise below. We also show how the theory p...
Restricting Fourier transforms of measures to curves in R^2
Fourier transforms of fractal measures Fourier restriction
2010/12/14
We establish estimates for restrictions to certain curves in R2 of the Fourier transforms of some fractal measures.