In this paper we prove that for a nonsingular projective variety of dimension at most 4 and with non-negative Kodaira dimension, the Kodaira dimension of coherent subsheaves of is bounded from above by the Kodaira dimension of the variety. This implies the finiteness of the fundamental group for such an provided that has vanishing Kodaira dimension and non-trivial holomorphic Euler characteristic.
W. Fulton and R. MacPherson posed the problem of unique existence of a bivariant Chern class-a Grothendieck transformation from the bivariant theory F of constructible functions to the bivariant homology theory H. J.-P. Brasselet proved the existence of a bivariant Chern class in the category of embeddable analytic varieties with cellular morphisms. In general however, the problem of uniqueness is still unresolved. In this paper we show that for morphisms having nonsingular target varieties there...
It is known that, under very general conditions, Blaschke products generate branched covering surfaces of the Riemann sphere. We are presenting here a method of finding fundamental domains of such coverings and we are studying the corresponding groups of covering transformations.
Soit un polynôme en deux variables, de degré et à coefficients entiers dans pour . Alors le nombre de zéros rationnels de est soit infini soit plus petit que . Nous montrons aussi une version plus générale sur les corps de nombres.
Nous montrons dans cet article des bornes pour la régularité de Castelnuovo-Mumford d’un schéma admettant des singularités, en fonction des degrés des équations définissant le schéma, de sa dimension et de la dimension de son lieu singulier. Dans le cas où les singularités sont isolées, nous améliorons la borne fournie par Chardin et Ulrich et dans le cas général, nous établissons une borne doublement exponentielle en la dimension du lieu singulier.
It is proved that there are only finitely many families of codimension two subvarieties not of general type in Q6.
Let X ⊂ P6 be a smooth irreducible projective threefold, and d its degree. In this paper we prove that there exists a constant β such that for all X containing a smooth ruled surface as hyperplane section and not contained in a fourfold of degree less than or equal to 15, d ≤ β. Under some more restrictive hypothesis we prove an analogous result for threefolds containing a smooth ruled surface as hyperplane section and contained in a fourfold of degree less than or equal to 15.