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3-folds of general type with K 3 = 4 p g - 14

Paola Supino (1999)

Bollettino dell'Unione Matematica Italiana

In questo lavoro vengono costruite famiglie di 3-folds algebriche e non singolari X di tipo generale tali che l'invariante K X 3 sia il minimo possibile rispetto al genere geometrico p g , quando si suppone che il morfismo canonico sia birazionale. Per tali 3-folds vale la relazione lineare K X 3 = 4 p g - 14 inoltre l'immagine del morfismo canonico é una varietà di Castelnuovo di P p g - 1 .

A 4₃ configuration of lines and conics in ℙ⁵

Tomasz Szemberg (1994)

Annales Polonici Mathematici

Studying the connection between the title configuration and Kummer surfaces we write explicit quadratic equations for the latter. The main results are presented in Theorems 8 and 16.

A Bogomolov property for curves modulo algebraic subgroups

Philipp Habegger (2009)

Bulletin de la Société Mathématique de France

Generalizing a result of Bombieri, Masser, and Zannier we show that on a curve in the algebraic torus which is not contained in any proper coset only finitely many points are close to an algebraic subgroup of codimension at least 2 . The notion of close is defined using the Weil height. We also deduce some cardinality bounds and further finiteness statements.

A classification theorem on Fano bundles

Roberto Muñoz, Luis E. Solá Conde, Gianluca Occhetta (2014)

Annales de l’institut Fourier

In this paper we classify rank two Fano bundles on Fano manifolds satisfying H 2 ( X , ) H 4 ( X , ) . The classification is obtained via the computation of the nef and pseudoeffective cones of the projectivization ( ) , that allows us to obtain the cohomological invariants of X and . As a by-product we discuss Fano bundles associated to congruences of lines, showing that their varieties of minimal rational tangents may have several linear components.

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