Algebraic Geometry

New submissions

Submissions received from Fri 28 Nov 08 to Mon 1 Dec 08, announced Tue, 2 Dec 08
[ total of 19 entries: 1-19 ]
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New submissions for Tue, 2 Dec 08

[1]  arXiv:0812.0032 [pdf, other]
Title: Homogeneous interpolation on ten points
Authors: Ciro Ciliberto, Rick Miranda
Comments: 36 pages
Subjects: Algebraic Geometry (math.AG)

In this paper we prove that for all pairs $(d,m)$ with $d/m \geq 174/55$, the linear system of plane curves of degree $d$ with ten general base points of multiplicity $m$ has the expected dimension.

[2]  arXiv:0812.0062 [ps, pdf, other]
Title: Configurations of infinitely near points
Authors: Antonio Campillo (AGT-UVA), Gerard Gonzalez-Sprinberg (IF), Francisco Monserrat (IUMPA-UPV)
Subjects: Algebraic Geometry (math.AG)

We present a survey of some aspects and new results on configurations, i.e. disjoint unions of constellations of infinitely near points, local and global theory, with some applications and results on generalized Enriques diagrams, singular foliations, and linear systems defined by clusters.

[3]  arXiv:0812.0169 [ps, pdf, other]
Title: Quantum Field Theories on Algebraic Curves and A. Weil Reciprocity Law
Authors: Leon A. Takhtajan
Comments: 45 pages
Subjects: Algebraic Geometry (math.AG); Quantum Algebra (math.QA); Representation Theory (math.RT)

Using Serre's adelic interpretation of the cohomology, we develop "differential and integral calculus" on an algebraic curve X over an algebraically closed constant field k of characteristic zero, define an algebraic analogs of additive and multiplicative multi-valued functions on X, and prove corresponding generalized residue theorem and A. Weil reciprocity law. Using the representation theory of global Heisenberg and lattice Lie algebras and the Heisenberg system, we formulate quantum field theories of additive, charged, and multiplicative bosons on an algebraic curve X. We prove that extension of the respected global symmetries - Witten's additive and multiplicative Ward identities - from the k-vector space of rational functions on X to the k-vector space of additive multi-valued functions, and from the multiplicative group of rational functions on X to the group of multiplicative multi-valued functions on X, defines these theories uniquely. The quantum field theory of additive bosons is naturally associated with the algebraic de Rham theorem and the generalized residue theorem, and the quantum field theory of multiplicative bosons - with the generalized A. Weil reciprocity law.

[4]  arXiv:0812.0254 [ps, pdf, other]
Title: On the Adams-Riemann-Roch theorem in positive characteristic
Authors: R. Pink, D. Rössler
Comments: 10 pages
Subjects: Algebraic Geometry (math.AG)

We give a new proof of the Adams-Riemann-Roch theorem for a smooth projective morphism in the situation where the base scheme is of characteristic $p>0$ and is regular and quasi-projective over a noetherian affine scheme. We also answer a question of B. K\"ock.

[5]  arXiv:0812.0271 [ps, pdf, other]
Title: Une conjecture sur la torsion des classes de Chern des fibrés de Gauss-Manin
Authors: V. Maillot, D. Rössler
Comments: 35 pages
Subjects: Algebraic Geometry (math.AG)

Pour tout $t\in\mN$ nous d\'efinissons un certain entier positif $\N_t$ et nous conjecturons: si $H$ est un fibr\'e de Gauss-Manin d'une fibration semi-stable alors la $t$-\`eme classe de Chern de $H$ est annul\'ee par $\N_t$. Nous d\'emontrons diverses cons\'equences de cette conjecture.
For any $t\in\mN$, we define a certain positive integer $\N_t$ and we conjecture: if $H$ is a Gauss-Manin bundle of a semi-stable fibration then the $t$-th Chern class of $H$ is kiled by $\N_t$. We prove various consequences of this conjecture.

[6]  arXiv:0812.0286 [ps, pdf, other]
Title: The projective McKay correspondence
Authors: Christopher Brav
Comments: 34 pages. To appear in International Mathematics Research Notices
Subjects: Algebraic Geometry (math.AG); Representation Theory (math.RT)

Kirillov has described a McKay correspondence for finite subgroups of PSL_{2}(C) that associates to each `height' function an affine Dynkin quiver together with a derived equivalence between equivariant sheaves on the projective line P^1 and representations of this quiver. The equivalences for different height functions are then related by reflection functors for quiver representations.
The main goal of this paper is to develop an analogous story for the cotangent bundle of P^1. We show that each height function gives rise to a derived equivalence between equivariant sheaves on the cotangent bundle T*P^1 and modules over the preprojective algebra of an affine Dynkin quiver. These different equivalences are related by spherical twists, which take the place of the reflection functors for P^1.

Cross-lists for Tue, 2 Dec 08

[7]  arXiv:0812.0066 (cross-list from math.SG) [ps, pdf, other]
Title: Potential functions via toric degenerations
Authors: Takeo Nishinou, Yuichi Nohara, Kazushi Ueda
Comments: 19 pages, no figures
Subjects: Symplectic Geometry (math.SG); Algebraic Geometry (math.AG)

This is a short companion paper to arXiv:0810.3470. We construct an integrable system on a Fano manifold from its flat degeneration into a toric Fano variety, and compute the potential function for its Lagrangian torus fibers.

[8]  arXiv:0812.0094 (cross-list from math.NT) [ps, pdf, other]
Title: A rank inequality for the Tate Conjecture over global function fields
Authors: Christopher Lyons
Comments: 16 pages; to appear in Expos. Math
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)

Following D. Ramakrishnan, we explain how L. Lafforgue's modularity theorem and an analytic theorem of H. Jacquet and J. Shalika can be applied to prove the following result related to the Tate Conjecture: for a smooth, projective, geometrically-connected variety defined over a global function field, the algebraic rank is less than or equal to the analytic rank.
Also discussed is the analogous (open) question for number fields and an easy extension of Lafforgue's theorem to remove the "finite-order character" assumption. All results are likely "known to the experts", but don't appear to be written down.

[9]  arXiv:0812.0112 (cross-list from math.NT) [ps, pdf, other]
Title: On families of (Phi,Gamma)-modules
Authors: Ruochuan Liu
Comments: 11 pages. Preliminary version. Comments are welcome
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)

We prove that every family of (overconvergent) \'etale (Phi,Gamma)-modules over a reduced affinoid algebra can be locally converted to a family of p-adic representations uniquely.

[10]  arXiv:0812.0221 (cross-list from math.DG) [ps, pdf, other]
Title: Singular monopoles on a flat circle bundle over a Riemann surface
Authors: Benoit Charbonneau, Jacques Hurtubise
Subjects: Differential Geometry (math.DG); Algebraic Geometry (math.AG)

In this paper, the moduli space of singular unitary monopoles on a the product of a circle and a Riemann surface is shown to correspond to a moduli space of stable pairs on the Riemann surface. These pairs consist of a holomorphic vector bundle on the surface and a meromorphic automorphism of the bundle. The singularities of this automorphism correspond to the singularities of the singular monopole. We then consider the complex geometry of the moduli space; in particular, we compute dimensions, both from the complex geometric and the gauge theoretic point of view.

Replacements for Tue, 2 Dec 08

[11]  arXiv:math/0703613 (replaced) [ps, pdf, other]
Title: Real Analytic Milnor Fibrations and a Strong Łojasiewicz Inequality
Authors: David B. Massey
Comments: 20 pages
Subjects: Algebraic Geometry (math.AG)
[12]  arXiv:0805.4083 (replaced) [ps, pdf, other]
Title: On the equi-normalizable deformations of singularities of complex plane curves
Authors: Dmitry Kerner
Comments: Minor changes of exposition. Some small results are added
Subjects: Algebraic Geometry (math.AG)
[13]  arXiv:0807.5135 (replaced) [ps, pdf, other]
Title: On some generalizations of Newton non degeneracy of hypersurface singularities
Authors: Dmitry Kerner
Comments: 13 pages; uses packages: amssymb,curves. Some new results are added, the exposition is improved
Subjects: Algebraic Geometry (math.AG)
[14]  arXiv:0808.1741 (replaced) [ps, pdf, other]
Title: D-bar Spark Theory and Deligne Cohomology
Authors: Ning Hao
Comments: 33 pages
Subjects: Algebraic Geometry (math.AG); Differential Geometry (math.DG)
[15]  arXiv:0809.2479 (replaced) [ps, pdf, other]
Title: Continuity of the radius of convergence of differential equations on $p$-adic analytic curves
Authors: Francesco Baldassarri
Subjects: Algebraic Geometry (math.AG); Number Theory (math.NT)
[16]  arXiv:0810.4859 (replaced) [ps, pdf, other]
Title: Gromov-Witten invariants for G/B and Pontryagin product for \Omega K
Authors: Naichung Conan Leung, Changzheng Li
Comments: 33 pages, a few modifications to the text and corrections to some minor mistakes. Submitted for publication
Subjects: Algebraic Geometry (math.AG); Combinatorics (math.CO)
[17]  arXiv:0811.2860 (replaced) [ps, pdf, other]
Title: Tropical rational equivalence on R^r
Authors: Lars Allermann, Johannes Rau
Comments: 6 pages, 2 figures; minor fixes in version 2
Subjects: Algebraic Geometry (math.AG); Combinatorics (math.CO)
[18]  arXiv:math/0601028 (replaced) [ps, pdf, other]
Title: On maximal proper subgroups of field automorphism groups
Authors: M. Rovinsky
Comments: 25 pages
Subjects: Representation Theory (math.RT); Algebraic Geometry (math.AG)
[19]  arXiv:0803.2809 (replaced) [ps, pdf, other]
Title: On a congruence problem of elliptic curves modulo $ p $
Authors: Qiu Derong
Comments: 15 pages, There is a slight change in Theorem 1, a new Theorem 2 and more results are added, some references are changed
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)
[ total of 19 entries: 1-19 ]
[ showing up to 2000 entries per page: fewer | more ]