Related papers: Fano threefolds with affine canonical extensions

We prove that any complete, embedded minimal surface $M$ with finite topology in a homogeneous three-manifold $N$ has positive injectivity radius. When one relaxes the condition that $N$ be homogeneous to that of being locally homogeneous,…

We classify compact K\"ahler manifolds with semi-positive holomorphic bisectional and big tangent bundles. We also classify compact complex surfaces with semi-positive tangent bundles and compact complex $3$-folds of the form $P(T^*X)$…

We study the question whether rational homogeneous spaces are rigid under Fano deformation. In other words, given any smooth connected family f:X -> Zof Fano manifolds, if one fiber is biholomorphic to a rational homogeneous space S,…

In this article, we prove that any $\Bbb Q$-factorial weak Fano 3-fold with only terminal singularities has a smoothing.

Let $f\colon X\to Y$ be a surjective morphism of Fano manifolds of Picard number 1 whose VMRTs at a general point are not dual defective. Suppose that the tangent bundle $T_X$ is big. We show that $f$ is an isomorphism unless $Y$ is a…

We classify smooth Fano threefolds with infinite automorphism groups.

We prove the Manin-Peyre conjecture for the number of rational points of bounded height outside of a thin subset on a family of Fano threefolds of bidegree (1,2). The proof uses a mixture of the circle method and techniques from the…

We give a classification of smooth Fano fourfolds such that the base scheme of the anticanonical system is a smooth surface. As a consequence we show that there are exactly 22 deformation families of such manifolds and they are all obtained…

We show that a compact Kahler manifold with nonpositive holomorphic sectional curvature has nef canonical bundle. If the holomorphic sectional curvature is negative then it follows that the canonical bundle is ample, confirming a conjecture…

We propose a conjectural list of Fano manifolds of Picard number $1$ with pseudoeffective normalized tangent bundles, which we prove in various situations by relating it to the complete divisibility conjecture of Russo and Zak on varieties…

In this paper, we prove the canonical bundle formula for Fano type fibrations and Shokurov's conjecture on boundedness of complements for Fano type threefold pairs $(X,B)$ with fibration structures in large characteristics. In particular,…

We study unirationality of actions of finite groups on Fano threefolds.

Let M be a (bounded or not) domain of C^n which is complete with respect to a K\"ahler metric, or more generally, a complete K\"ahler manifold with trivial canonical bundle. Let f be a linearly nondegenerate meromorphic map from M to the…

An affine manifold is a manifold with an affine structure, i.e. a torsion-free flat affine connection. We show that the universal cover of a closed affine 3-manifold $M$ with holonomy group of shrinkable dimension (or discompacit\'e in…

A Fano manifold $X$ with nef tangent bundle is of flag-type if it has the same type of elementary contractions as a complete flag manifold. In this paper we present a method to associate a Dynkin diagram $\mathcal{D}(X)$ with any such $X$,…

The goal of this short note is to point out that every Fano manifold with a nef tangent bundle possesses an almost K{\"a}hler-Einstein metric, in a weak sense. The technique relies on a regularization theorem for closed positive (1,…

We study rational curves on general Fano hypersurfaces in projective space, mostly by degenerating the hypersurface along with its ambient projective space to reducible varieties. We prove results on existence of low-degree rational curves…

This paper was written in 1982. Ideas and methods of "Clemens C.H., Griffiths Ph. The intermediate Jacobian of a cubic threefold" are applied to a Fano threefold X of genus 6 -- intersection of Grassmann sixfold with two hyperplanes and a…

We prove the $W\mathcal{O}$-rationality of klt threefolds and the rational chain connectedness of klt Fano threefolds over a perfect field of characteristic $p>5$. As a consequence, any klt Fano threefold over a finite field has a rational…

We introduce and we study a class of odd dimensional compact complex manifolds whose Hodge structure in middle dimension looks like that of a Calabi-Yau threefold. We construct several series of interesting examples from rational…