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Let $X$ be a Fano manifold with $b_{2} = 1$ different from the projective space such that any two surfaces in $X$ have proportional fundamental classes in $H_{4} (X, C)$ . Let $f : Y \to X$ be a surjective holomorphic map from a projective variety $Y$ . We show that all deformations of $f$ with $Y$ and $X$ fixed, come from automorphisms of $X$ . The proof is obtained by studying the geometry of the integral varieties of the multi-valued foliation defined by the variety of minimal rational tangents of $X$ .

Deformation of Varieties Defined by Sections in Homogeneous Vector Bundles.

Joachim Wehler (1984)

Mathematische Annalen

Deformations of cones over hyperelliptic curves.

Jan Stevens (1995)

Journal für die reine und angewandte Mathematik

Deformations of Quasi-Homogeneous Surface Singularities.

Jonathan Wahl (1988)

Mathematische Annalen

Deformations of ruled mainfolds.

Alexander Schmitt (1995)

Journal für die reine und angewandte Mathematik

Deformations of ruled surfaces.

Wolfgang K. Seiler (1992)

Journal für die reine und angewandte Mathematik

Deformations of Weierstraß Elliptic Surfaces.

Wolfgang K. Seiler (1988)

Mathematische Annalen

Degeneracy of holomorphic maps via orbifolds

Erwan Rousseau (2012)

Bulletin de la Société Mathématique de France

We use orbifold structures to deduce degeneracy statements for holomorphic maps into logarithmic surfaces. We improve former results in the smooth case and generalize them to singular pairs. In particular, we give applications on nodal surfaces and complements of singular plane curves.

Currently displaying 1 – 20 of 54

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Displaying 1 – 20 of 54

$D$ -dimensions of algebraic surfaces and numerically effective divisors

Defect series and nonrational Hilbert modular threefolds.

Defects of Cusp Singularities.

Defects of cusp singularities and the classification of Hilbert modular threefolds.

Déformation d'une singularité isolée d'hypersurface et polynômes de Bernstein

Deformation of holomorphic maps onto Fano manifolds of second and fourth Betti numbers 1

Deformation of Varieties Defined by Sections in Homogeneous Vector Bundles.

Deformations of cones over hyperelliptic curves.

Deformations of Quasi-Homogeneous Surface Singularities.

Deformations of ruled mainfolds.

Deformations of ruled surfaces.

Deformations of Weierstraß Elliptic Surfaces.

Degeneracy of holomorphic maps via orbifolds

Degenerations of Horrocks-Mumford Surfaces.

Degré de la variété duale d'une hypersurface à singularités isolées

Del Pezzo surfaces of degree four

Density of rational points on elliptic surfaces

Der Flächenbüschel zweiter Ordnung in synthetischer Behandlung. Von H. Müller in Freiburg i. Br.

Derivations of Negative Weight and Non-Smoothability of Certain Singularities.

Descente et principe de Hasse pour certaines variétés rationnelles.

Currently displaying 1 – 20 of 54