ETD

Archivio digitale delle tesi discusse presso l'Università di Pisa

Tesi etd-09042018-111916


Tipo di tesi
Tesi di laurea magistrale
Autore
GRAFFEO, MICHELE
URN
etd-09042018-111916
Titolo
Koszul cohomology and Hilbert schemes of points
Dipartimento
MATEMATICA
Corso di studi
MATEMATICA
Relatori
relatore Prof. Franciosi, Marco
controrelatore Prof. Manfredini, Sandro
Parole chiave
  • Koszul cohomology
  • K3 surfaces
  • Hilbert scheme
  • Green's conjecture
  • Brill-noether theory
  • Mukai-Lazarsfeld bundle
  • Voisin's theorem
Data inizio appello
21/09/2018
Consultabilità
Completa
Riassunto
Since 1984, year in which it was rst formulated, Green's conjecture has been object of study in algebraic geometry research: my master thesis is devoted to Clair Voisin's solution to such problem.
In particular, Green's conjecture solution stems, as a corollary, from a more general theorem by Voisin.
The most relevant concepts this thesis touches upon are:
Hilbert schemes of point, the Cayley-Bacharach property, the Mukai-Lazarsfeld bundle, the Koszul cohomology and the K3 surfaces.
Being this work a descriptive thesis, it does not lead to any innovative results. However, having built and proved myself most of the theorems and demonstrations covered in the first three chapters, I managed to get in-depth knowledge and get considerably familiarised with many tools and topics typical of modern algebraic geometry.
This thesis contributes to the literature in that it is, leaving Aprodu & Nagel ([2010] chapters 4-6) and Voisin ([2002]) aside, the rst paper fully dedicated to the theorem.
This means that it extensively articulates crucial aspects of the theory that Voisin ([2002]) only quickly touches upon.
In particular, to work on this thesis allowed me to study concepts and focus on some research areas that I had not have the chance to study during my bachelor and master classes.
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