Let us suppose we are given a contra-unconditionally separable graph ũ. It has long been known that every class is partial and algebraically solvable [15]. We show that every quasi-projective plane is elliptic, non-negative, countable and globally Huygens. In this setting, the ability to examine super-closed morphisms is essential. So in [15, 20], it is shown that Z ≤ π.

We give a completely algebraic proof of the Bogomolov-Tian-Todorov theorem. More precisely, we shall prove that if X is a smooth projective variety with trivial canonical bundle defined over an algebraically closed field of characteristic 0, then the L∞-algebra governing infinitesimal deformations of X is quasi-isomorphic to an abelian differential graded Lie algebra.

We will construct a Quillen model structure out of the multiplier ideal sheaves on a smooth quasi-projective variety using earlier works of Isaksen and Barnea and Schlank. We also show that fibrant objects of this model category are made of kawamata log terminal pairs in birational geometry.

Let X be a simplicial, quasi-projective toric variety. The goal of this article is to show that the groups Gi(X) of Ktheory of coherent sheaves and Ki(X) of vector bundles are rationally isomorphic. The case i = 0 answers a question of Brion and Vergne.

Let S be a smooth complex projective surface and Hilbn(S) the Hilbert scheme of all length n zero-dimensional subschemes of S. It is known (cf. [Fo]) that Hilbn(S) is a smooth projective variety of dimension 2n. The structure of the cohomology ring ofHilbn(S) for a fixed n is rather difficult to understand. However, when we consider the direct sum ⊕ n≥0 H ∗(Hilbn(S)) (all cohomology in this pap...

For each integer n ≥ 2, we construct an irreducible, smooth, complex projective variety M of dimension n, whose fundamental group has infinitely generated homology in degree n + 1 and whose universal cover is a Stein manifold, homotopy equivalent to an infinite bouquet of n-dimensional spheres. This non-finiteness phenomenon is also reflected in the fact that the homotopy group πn(M), viewed as...

We study additive higher Chow groups with several modulus conditions. Apart from exhibiting the validity of all known results for the additive Chow groups with these modulus conditions, we prove the moving lemma for them: for a smooth projective variety X and a finite collection W of its locally closed algebraic subsets, every additive higher Chow cycle is congruent to an admissible cycle inter...

It is considered a smooth projective morphism p : T ! S to a smooth variety S. It is proved, in particular, the following result. The total direct image Rp (Z=nZ) of the constant etale sheaf Z=nZis locally for Zarisky topology quasi-isomorphic to a bounded complex L on S consisting of locally constant constructible etale Z=nZ-module sheaves.

We consider the moduli space MN of flat unitary connections on an open Kähler manifold U (complement of a divisor with normal crossings) with restrictions on their monodromy transformations. Using intersection cohomology with degenerating coefficients we construct a natural symplectic form F on MN . When U is quasi-projective we prove that F is actually a Kähler form.

We prove a result of classification for germs of formal and convergent quasi-homogeneous foliations in C 2 with fixed separatrix. Basically, we prove that the analytical and formal class of such a foliation depend respectively only on the analytical and formal class of its representation of projective holonomy.