Related papers: Birational geometry of defective varieties

We study the birational geometry of hypersurfaces in products of weighted projective spaces, extending results previously established by J. C. Ottem. For most cases where these hypersurfaces are Mori dream spaces, we determine all relevant…

We investigate the secant dimensions and the identifiablity of flag varieties parametrizing flag of sub vector spaces of a fixed vector space. We give numerical conditions ensuring that secant varieties of flag varieties have the expected…

We study equivariant birationality from the perspective of derived categories. We produce examples of nonlinearizable but stably linearizable actions of finite groups on smooth cubic fourfolds.

We compute the Kodaira dimension of the universal Picard variety P_{d,g} parameterizing line bundles of degree d on curves of genus g under the assumption that (d-g+1,2g-2)=1. We also give partial results for arbitrary degrees d and we…

We survey some aspects of stability conditions both in general and on the derived category of coherent sheaves on a surface, with applications to the birational geometry of certain holomorphic symplectic varieties.

We construct a family of birational maps acting on two dimensional projective varieties, for which the growth of the degrees of the iterates is cubic. It is known that this growth can be bounded, linear, quadratic or exponential for such…

We investigate geometry of D-affine varieties. Our main result is that a D-affine rational projective surface over an algebraically closed field is a generalised flag variety of a reductive group.

We study $G$-equivariant birational geometry of toric varieties, where $G$ is a finite group.

We investigate Gauss maps of (not necessarily normal) projective toric varieties over an algebraically closed field of arbitrary characteristic. The main results are as follows: (1) The structure of the Gauss map of a toric variety is…

Various methods have been used to construct rational points and rational curves on rationally connected algebraic varieties. We survey recent advances in two of them, the descent and the fibration method, in a number-theoretical context…

We give an elementary introduction to our papers relating the geometry of rational homogeneous varieties to representation theory. We also describe related work and recent progress.

We shall show how to decompose, by functorial and canonical fibrations, arbitrary $n$-dimensional complex projective {Although the geometric results apply to compact K\" ahler manifolds without change, we consider here for simplicity this…

We study projective varieties whose universal cover is biholomorphic to a semialgebraic open subset of a projective variety.

We construct normal rationally connected varieties (of arbitrarily large dimension) not containing any smooth rational curves.

We develop an intersection theory for a singular hemitian line bundle with positive curvature current on a smooth projective variety and irreducible curves on the variety. And we prove the existence of a natural rational fibration structure…

In this paper we analyse the birational geometry of O'Grady ten dimensional manifolds, giving a characterisation of Kaehler classes and lagrangian fibrations. Moreover, we study symplectic compactifications of intermediate jacobian…

We provide a classification of complex projective surfaces with a holomorphic foliation whose group of birational symetries is infinite.

We define a birational version of the stability of cotangent sheaves for complex projective manifolds, and more generally for smooth orbifolds. We then show, using standard conjectures in birational classification, that these cotangent…

In this paper, we investigate the explicit birational geometry for projective $\epsilon$-lc varieties polarised by nef and big Weil divisors. We show that if $X$ is a projective $\epsilon$-lc variety, $H$ is a nef and big Weil divisor with…

We propose a study of the foliations of the projective plane induced by simple derivations of the polynomial ring in two indeterminates over the complex field. These correspond to foliations which have no invariant algebraic curve nor…