Closedness of regular -forms on algebraic surfaces
Closure Theorem for Partially Semialgebraic Sets
In 1988 it was proved by the first author that the closure of a partially semialgebraic set is partially semialgebraic. The essential tool used in that proof was the regular separation property. Here we give another proof without using this tool, based on the semianalytic L-cone theorem (Theorem 2), a semianalytic analog of the Cartan-Remmert-Stein lemma with parameters.
Closures of Conjugacy Classes of Matrices are Normal.
Closures of SL(2)-Orbits in Projective Spaces.
Clôture intégrale des idéaux et équisingularité
This text has two parts. The first one is the essentially unmodified text of our 1973-74 seminar on integral dependence in complex analytic geometry at the Ecole Polytechnique with J-J. Risler’s appendix on the Łojasiewicz exponents in the real-analytic framework. The second part is a short survey of more recent results directly related to the content of the seminar.The first part begins with the definition and elementary properties of the order function associated to an ideal of a reduced analytic...
Cluster ensembles, quantization and the dilogarithm
A cluster ensemble is a pair of positive spaces (i.e. varieties equipped with positive atlases), coming with an action of a symmetry group . The space is closely related to the spectrum of a cluster algebra [12]. The two spaces are related by a morphism . The space is equipped with a closed -form, possibly degenerate, and the space has a Poisson structure. The map is compatible with these structures. The dilogarithm together with its motivic and quantum avatars plays a central role...
Clusters of infinitely near points.
CM points and quaternion algebras.
Coarse moduli space of ordinary multiple points in the plane.
Coates-Wiles Towers in Dimension Two.
Cobordism of algebraic knots via Seifert forms.
Cobordisme des variétés algébriques
Codes de Goppa
Codescente en K-théorie étale et corps de nombres.
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 2 subvarieties of projective space.
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 .
Codimension two transcendental submanifolds of projective space
We provide a simple characterization of codimension two submanifolds of that are of algebraic type, and use this criterion to provide examples of transcendental submanifolds when . If the codimension two submanifold is a nonsingular algebraic subset of whose Zariski closure in is a nonsingular complex algebraic set, then it must be an algebraic complete intersection in .
Codimension-two Subvarieties of IPn with the Cohomology of a Complete Intersection.
Codimesion two linear varieties with nilpotent structures.