Carolina Araujo

Cohomological characterizations of projective spaces and hyperquadrics

Projective spaces and hyperquadrics are the simplest projective algebraic varieties, and they can be characterized in many ways. The aim of this paper is to provide a new characterization of them in terms of positivity properties of the tangent bundle (Theorem 1.1). The first result in this direction was Mori’s proof of the Hartshorne conjecture in [Mor79] (see also Siu and Yau [SY80]), that characterizes projective spaces as the only manifolds having ample tangent bundle. Then, in [Wah83], Wahl characterized projective spaces as the only manifolds whose tangent bundles contain ample invertible subsheaves. Interpolating Mori’s and Wahl’s results, Andreatta and Wiśniewski gave the following characterization:

The cone of pseudo-effective divisors of log varieties after Batyrev

In these notes, we investigate the cone of nef curves of projective varieties, which is the dual cone to the cone of pseudo-effective divisors. We prove a structure theorem for the cone of nef curves of projective

On degeneracy schemes of maps of vector bundles and applications to holomorphic foliations

{\mathbb Q}

On Smooth Lattice Polytopes with Small Degree

-factorial klt pairs of arbitrary dimension from the point of view of the Minimal Model Program. This is a generalization of Batyrev’s structure theorem for the cone of nef curves of projective terminal threefolds.

Rational curves of minimal degree and characterizations of projective spaces

In this paper we determine which blow-ups

On Fano foliations

X

On codimension 1 del Pezzo foliations on varieties with mild singularities

of

Identifying quadric bundle structures on complex projective varieties

\mathbb{P}^n