Flag Manifolds and Toric Geometry

Lectures on complex geometry, Calabi–Yau manifolds and toric geometry

These are introductory lecture notes on complex geometry, Calabi–Yau manifolds and toric geometry. We first define basic concepts of complex and Kähler geometry. We then proceed with an analysis of various definitions of Calabi–Yau manifolds. The last section provides a short introduction to toric geometry, aimed at constructing Calabi–Yau manifolds in two different ways; as hypersurfaces in to...

On the k-nullity foliations in Finsler geometry

Here, a Finsler manifold $(M,F)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. Certain subspaces of the tangent spaces of $M$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. It is shown that if the dimension of foliation is constant, then the distribution is involutive...

Symplectic Toric Manifolds

Foreword These notes cover a short course on symplectic toric manifolds, delivered in six lectures at the summer school on Symplectic Geometry of Integrable Hamiltonian Systems, mostly for graduate students, held at the Centre de Recerca Matemàtica in Barcelona in July of 2001. The goal of this course is to provide a fast elementary introduction to toric manifolds (i.e., smooth toric varieties)...

Kahler geometry on toric manifolds , and some other manifolds with large symmetry

TORIC MORI THEORY AND FANO MANIFOLDS by Jaros law

— The following are the notes to five lectures on toric Mori theory and Fano manifolds given during the school on toric geometry which took place in Grenoble in Summer of 2000.