Challenging problems on affine -space
Chamber structures of algebraic surfaces with Kodaira dimension zero and moduli spaces of stable rank two bundles.
Change of polarization and Hodge numbers of moduli spaces of torsion free sheaves on surfaces.
Character sums in finite fields
Characteres and Galois invariants of regular dessins.
We describe a new invariant for the action of the absolute Galois groups on the set of Grothendieck dessins. It uses the fact that the automorphism groups of regular dessins are isomorphic to automorphism groups of the corresponding Riemman surfaces and define linear represenatations of the space of holomorphic differentials. The characters of these representations give more precise information about the action of the Galois group than all previously known invariants, as it is shown by a series...
Characterisation des variétés compactes simplifiables et applications aux surfaces algébriques.
Characteristic Classes of Kuga Fiber Varieties of Quaternion Type.
Characteristic divisors on complex manifolds.
Characteristic varieties and vanishing cycles.
Characteristic varieties of character sheaves.
Characterization of abelian varieties
Characterization of compact subsets of algebraic varieties in terms of Bernstein type inequalities
We show that in the class of compact sets K in with an analytic parametrization of order m, the sets with Zariski dimension m are exactly those which admit a Bernstein (or a van der Corput-Schaake) type inequality for tangential derivatives of (the traces of) polynomials on K.
Characterization of jacobian Newton polygons of plane branches and new criteria of irreducibility
In this paper we characterize, in two different ways, the Newton polygons which are jacobian Newton polygons of a plane branch. These characterizations give in particular combinatorial criteria of irreducibility for complex series in two variables and necessary conditions which a complex curve has to satisfy in order to be the discriminant of a complex plane branch.
Characterization of jacobian varieties in arbitrary characteristic
Characterization of Jacobian varieties in terms of soliton equations.
Characterization of non-degenerate plane curve singularities.
Characterization of smooth, compact algebraic curves in ℝ²
Characterization of the complex projective space by holomorphic vector fields.
Characterization of the Hilbert-Samuel polynomials of curve singularities
Characterizations of certain singularities of a branched covering