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Soit $X$ une variété algébrique projective lisse irréductible. On appelle variété de modules fins de faisceaux sur $X$ une famille $ℱ$ de faisceaux cohérents sur $X$ paramétrée par une variété intègre $M$ , possédant les propriétés suivantes : $ℱ$ est plate sur $M$ ; pour tous $x, y \in M$ distincts, les faisceaux $ℱ_{x}$ et $ℱ_{y}$ sur $X$ ne sont pas isomorphes et $ℱ$ est une déformation complète de $ℱ_{x}$ ; enfin $ℱ$ possède une propriété universelle locale évidente. On a aussi la notion de variété de modules fins définie localement, où $ℱ$ est...

Varieties of minimal rational tangents of codimension 1

Jun-Muk Hwang (2013)

Annales scientifiques de l'École Normale Supérieure

Let $X$ be a uniruled projective manifold and let $x$ be a general point. The main result of [2] says that if the $(- K_{X})$ -degrees (i.e., the degrees with respect to the anti-canonical bundle of $X$ ) of all rational curves through $x$ are at least $dim X + 1$ , then $X$ is a projective space. In this paper, we study the structure of $X$ when the $(- K_{X})$ -degrees of all rational curves through $x$ are at least $dim X$ . Our study uses the projective variety $𝒞_{x} \subset ℙ T_{x} (X)$ , called the VMRT at $x$ , defined as the union of tangent directions to the rational curves...

Varieties of small Kodaira dimension whose cotangent bundles are semiample

Tsuyoshi Fujiwara (1992)

Compositio Mathematica

Varieties whose hyperplane section are $ℙ_{ℂ}^{k}$ bundles

Maria Lucia Fania, Andrew John Sommese (1988)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Varieties with generically nef tangent bundles

Thomas Peternell (2012)

Journal of the European Mathematical Society

We study various "generic" nefness and ampleness notions for holomorphic vector bundles on a projective manifold. We apply this in particular to the tangent bundle and investigate the relation to the geometry of the manifold.

Zariski surfaces [Book]

Piotr Blass (1983)

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Über eine topologische und zahlentheoretische Anwendung von Hirzebruchs Spitzenauflösung.

Ueber die allgemeinste Flächenschaar zweiten Grades, die mit irgend zwei andern Flächenschaaren ein orthogonales System bildet.

Une précision concernant le théorème de Noether.

Van Geemen's Families of lines on special quintic threefolds.

Variation of moduli spaces and Donaldson invariants under change of polarization.

Varietà di Fano di dimensione $n$ > $4$ e di indice $r$ > $n - 1$

Variétés de Fano

Variétés de modules alternatives

Varieties of minimal rational tangents of codimension 1

Varieties of small Kodaira dimension whose cotangent bundles are semiample

Varieties whose hyperplane section are $ℙ_{ℂ}^{k}$ bundles

Varieties with generically nef tangent bundles

Varieties with $P_{3} (X) = 4$ and $q (X) =$ dim $(X)$

Weak positivity and the stability of certain Hilbert points, III.

Weak positivity and the stability of certain Hilbert points.

Weak positivity and the stability of certain Hilbert points, II.

Zariski surfaces [Book]

Zur Klassifikation von Regelmannigfaltigkeiten.

Многообразия Гильберта-Куги-Сато и параболические дифференциалы

О бирациональной эквивалентности торов с циклическим полем разложения

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