Simone Marchesi

• Abstract

  This research project focuses on the study of vector bundles on smooth projective varieties.\\The first topic of research consists in the definition and the study of the concept of \textit{Kronecker Module} for instanton bundles on Flag varieties. This definition will help us understand better the jumping conic locus and their moduli spaces.\\The second topic of research focuses on the st…

  Hyperplane arrangements, foliations and Kronecker modules, AP.R

• Abstract

  The goal of this project is to focus on one of the most famous conjectures in the study of hyperplanes arrangements: the so called Terao's Conjecture, asserting that the freeness of an arrangement depends only on its combinatorics, in other words on the incidence relations between its hyperplanes. We will recall the necessary definitions to introduce the conjecture and we will explain whi…

  Arrangements and vector bundles, AV.EXT

• Abstract

  This research project focuses on the study of vector bundles on smooth projective varieties. The first topic consists in the study of the family of orthogonal instanton bundles on projective spaces. We will generalize the already known description, called the net of quadrics in the symplectic case, for the orthogonal one. Our goal is to find new examples, non-existence results and a descr…

  Vector bundles: from the instanton family to a new regularity, AP.R

(Only some records are available in English at this moment)

• Abstract

  We aim to extend and reinforce the knowledge of the beneficiary in the foundations of algebraic geometry, studying subjects relevant to contemporary research, and to have an introduction in Liaison Theory; having as final objective the study of "Intersection of ACM-Curves in P3", written by Miró-Roig and Ranestad, an article concerning the intersection of arithmetically Cohen-Macauly curv…

  An introduction to Liaison Theory, BP.MS

• Abstract

  The goal of this project is the study of projective geometry followed by an introduction on the concepts of vector bundle and Grassmannian, and their relations in order to study the subvarieties of the Grassmannian. (AU)

  Vector bundles and grassmannians, BP.IC

• Abstract

  The goal of this project is to give to the student an introduction of algebraic geometry. In particular, this one has a more geometrical focus, centered in the study of algebraic plane curves. Nevertheless, during this oriented studying, we will also give a look to the commutative algebra part and the basic concepts of algebraic geometry in a general setting. (AU)

  Algebraic plane curves: Bezout´s theorem, BP.IC

(Only some records are available in English at this moment)

• Abstract

  We aim to extend the knowledge of the beneficiary in algebraic geometry, focusing in the concepts of Instanton and ACM bundles, studying the necessary basis to attack original and actual problems in this context. (AU)

  Instanton bundles and ACM bundles, BE.EP.MS

• Abstract

  We will introduce the notion of generalized instanton bundle and study its properties. In particular, we will focus on the study of the moduli space of stable vector bundle of rank 2 over the three dimensional projective space. The goals of our work will be:-determine how many irreducible components such moduli space has;-determine its dimension. (AU)

  Moduli space of generalized instanton bundles, BE.EP.PD