Characterization of the Hilbert-Samuel polynomials of curve singularities
Characterizing Curves on Surface of Special Types.
Chen–Ruan Cohomology of and
In this work we compute the Chen–Ruan cohomology of the moduli spaces of smooth and stable -pointed curves of genus . In the first part of the paper we study and describe stack theoretically the twisted sectors of and . In the second part, we study the orbifold intersection theory of . We suggest a definition for an orbifold tautological ring in genus , which is a subring of both the Chen–Ruan cohomology and of the stringy Chow ring.
Class Group Rank Relations in Zl-Extensions.
Class numbers of quadratic fields and Shimura's correspondence.
Classes d'idéaux et classes de diviseurs
Classification of degree 2 polynomial automorphisms of C3.
For the family of degree at most 2 polynomial self-maps of C3 with nowhere vanishing Jacobian determinant, we give the following classification: for any such map f, it is affinely conjugate to one of the following maps:(i) An affine automorphism;(ii) An elementary polynomial autormorphismE(x, y, z) = (P(y, z) + ax, Q(z) + by, cz + d),where P and Q are polynomials with max{deg(P), deg(Q)} = 2 and abc ≠ 0.(iii)⎧ H1(x, y, z) = (P(x, z) + ay, Q(z) + x, cz + d)⎪ H2(x, y, z) = (P(y, z) + ax, Q(y)...
Classification of Maximal Rank Curves in the Liasion Class Ln.
Clifford’s Theorem for real algebraic curves
We establish, for smooth projective real curves, an analogue of the classical Clifford inequality known for complex curves. We also study the cases when equality holds.
Codes de Goppa
Codimension 1 subvarieties and real gonality of real curves
Let be the moduli space of smooth complex projective curves of genus . Here we prove that the subset of formed by all curves for which some Brill-Noether locus has dimension larger than the expected one has codimension at least two in . As an application we show that if is defined over , then there exists a low degree pencil defined over .
Codimension Arithmetically Gorenstein Subschemes of projective -space
We study the lowest dimensional open case of the question whether every arithmetically Cohen–Macaulay subscheme of is glicci, that is, whether every zero-scheme in is glicci. We show that a general set of points in admits no strictly descending Gorenstein liaison or biliaison. In order to prove this theorem, we establish a number of important results about arithmetically Gorenstein zero-schemes in .
Co-fibered products of algebraic curves
We give examples of failure of the existence of co-fibered products in the category of algebraic curves.
Cohen-Macaulay liason.
Cohen-Macaulay module type
Coherent sheaves with parabolic structure and construction of Hecke eigensheaves for some ramified local systems
The aim of these notes is to generalize Laumon’s construction [20] of automorphic sheaves corresponding to local systems on a smooth, projective curve to the case of local systems with indecomposable unipotent ramification at a finite set of points. To this end we need an extension of the notion of parabolic structure on vector bundles to coherent sheaves. Once we have defined this, a lot of arguments from the article “ On the geometric Langlands conjecture” by Frenkel, Gaitsgory and Vilonen [11]...
Cohomologie des courbes elliptiques
Cohomology of desingularization of moduli space of vector bundles
Cohomology of moduli spaces of stable curves.
Combinations of rational singularities on plane sextic curves with the sum of Milnor numbers less than sixteen