Limits of Calabi–Yau metrics when the Kähler class degenerates
2000 Mathematics Subject Classification: 14H45, 14H50, 14J26.We construct linearly normal curves covering a big range from P^n, n ≥ 6 (Theorems 1.7, 1.9). The problem of existence of such algebraic curves in P^3 has been solved in [4], and extended to P^4 and P^5 in [10]. In both these papers is used the idea appearing in [4] and consisting in adding hyperplane sections to the curves constructed in [6] (for P^3) and [15, 11] (for P^4 and P^5) on some special surfaces. In the present paper we apply...
Lines on hypersurfaces with isolated singularities are classified. New normal forms of simple singularities with respect to lines are obtained. Several invariants are introduced.
Soient un espace analytique affinoïde réduit sur un corps complet pour une valeur absolue non archimédienne, sa réduction canonique et un point de la variété algébrique affine . Ce travail décrit la singularité du point à l’aide d’objets associés à l’espace : la localisation formelle qui est une -algèbre noethérienne de spectre maximal et dont la réduction est ; un complété formel qui est une -algèbre noethérienne dont la réduction est . Les résultats essentiels sont obtenus...
In 1981 J. Noguchi proved that in a logarithmic algebraic manifold, having logarithmic irregularity strictly bigger than its dimension, any entire curve is algebraically degenerate.In the present paper we are interested in the case of manifolds having logarithmic irregularity equal to its dimension. We restrict our attention to Brody curves, for which we resolve the problem completely in dimension 2: in a logarithmic surface with logarithmic irregularity and logarithmic Kodaira dimension , any...