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Systèmes linéaires adjoints L 2

Philippe Eyssidieux (1999)

Annales de l'institut Fourier

Nous développons une version de la théorie d’indice L 2 d’Atiyah pour les faisceaux cohérents sur les variétés algébriques lisses et l’utilisons pour attaquer certaines questions de J. Kollár.Soit X une variété complexe compacte projective algébrique lisse et connexe. Nous prouvons que si L est un diviseur nef et gros, tel que la restriction de K X + L à la fibre générale d’une application de Shafarevich est effective, K X + L est effectif.Soit X une variété kählérienne compacte telle qu’il existe une classe...

The Fujiki class and positive degree maps

Gautam Bharali, Indranil Biswas, Mahan Mj (2015)

Complex Manifolds

We show that a map between complex-analytic manifolds, at least one ofwhich is in the Fujiki class, is a biholomorphism under a natural condition on the second cohomologies. We use this to establish that, with mild restrictions, a certain relation of “domination” introduced by Gromov is in fact a partial order.

The growth of regular functions on algebraic sets

A. Strzeboński (1991)

Annales Polonici Mathematici

We are concerned with the set of all growth exponents of regular functions on an algebraic subset V of ℂ n . We show that its elements form an increasing sequence of rational numbers and we study the dependence of its structure on the geometric properties of V.

The pro-unipotent radical of the pro-algebraic fundamental group of a compact Kähler manifold

Jonathan Pridham (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

The aim of this paper is to study the pro-algebraic fundamental group of a compact Kähler manifold. Following work by Simpson, the structure of this group’s pro-reductive quotient is already well understood. We show that Hodge-theoretic methods can also be used to establish that the pro-unipotent radical is quadratically presented. This generalises both Deligne et al.’s result on the de Rham fundamental group, and Goldman and Millson’s result on deforming representations of Kähler groups, and can...

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