Related papers: The nef dimension of log minimal models
An extended version of a series of lectures given at Bogota in december 2002. It consists in a presentation of some aspects of Connes' and Kreimer's work on renormalization in the context of general connected Hopf algebras, in particular…
On June 5, 2007 the second author delivered a talk at the Journees de l'Institut Elie Cartan entitled "Finite symmetry groups in complex geometry". This paper begins with an expanded version of that talk which, in the spirit of the…
This document contains notes from the lectures of Corti, Koll\'ar, Lazarsfeld, and Musta\c{t}\u{a} at the workshop ``Minimal and canonical models in algebraic geometry" at MSRI, Berkeley, April 2007. The lectures give an overview of the…
The Hodge decomposition provides a very powerful mathematical method for the analysis of 2D and 3D vector fields. It states roughly that any vector field can be $L^2$-orthogonally decomposed into a curl-free, divergence-free, and a harmonic…
In this paper an extended CPR decomposition theorem for Finsler symmetric spaces of semi-negative curvature in the context of reductive structures is proven. This decomposition theorem is applied to give a geometric description of the…
All complex $3$-dimensional nilalgebras were described. As a corollary, all degenerations in the variety of complex $3$-dimensional nilalgebras were obtained.
This is an expository paper which explores the ideas of the authors' paper "From Affine Geometry to Complex Geometry", arXiv:0709.2290. We explain the basic ideas of the latter paper by going through a large number of concrete, increasingly…
This talk, dedicated to Eef van Beveren on the occasion of his birthday, reviews some of our results concerning the hadron spectroscopy, Regge trajectories, and the large-Nc meson-dominance of hadronic form factors.
The problems concerning a possible discovery of the mini block holes at earthly accelerators are discussed.
We construct exceptional Fano varieties with the smallest known minimal log discrepancies in all dimensions. These varieties are well-formed hypersurfaces in weighted projective space. Their minimal log discrepancies decay doubly…
Concluding talk, Physics at LHC 2004, Vienna
Proceedings of DISCRETE 2010, Symposium on Prospects in the Physics of Discrete Symmetries, Rome (IT), 6-11 December 2010
We prove that the existence of log minimal models in dimension $d$ essentially implies the LMMP with scaling in dimension $d$. As a consequence we prove that a weak nonvanishing conjecture in dimension $d$ implies the minimal model…
A talk presented at International Conference ICMP-2000, London, England
This is a contribution to the proceedings of the 2016 "Loops and legs" conference, based on the talk by HF. The talk was based on the paper "On the reduction of Generalized Polylogarithms to $\text{Li}_n$ and $\text{Li}_{2,2}$ and on the…
This paper is based on a course given by the author at the University of Rome ``La Sapienza'' in the Academic year 2000/2001. The intended aim of the course was to rapidly introduce, although not in an exhaustive way, the non-expert PhD…
This is a written-up version of eight introductory lectures to the Hodge theory of projective manifolds. The table of contents should be self-explanatory. The only exception is section 8 where I discuss, in a simple example, a technique for…
This thesis is divided into two parts. In the first part we study completely integrable systems, and their underlying structures, in detail. We study their deformation theory and the different equivalence relations surrounding it. We…
We generalize a result of Fujita, on the decomposition of Hodge bundles over curves, to the case of a higher dimensional base.
Given an irreducible well-generated complex reflection group, we construct an explicit basis for the module of vector fields with logarithmic poles along its reflection arrangement. This construction yields in particular a Hodge filtration…