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Archivio digitale delle tesi discusse presso l’Università di Pisa

Tesi etd-06292009-165906


Tipo di tesi
Tesi di laurea specialistica
Autore
TALPO, MATTIA
URN
etd-06292009-165906
Titolo
Deformation theory
Dipartimento
SCIENZE MATEMATICHE, FISICHE E NATURALI
Corso di studi
MATEMATICA
Relatori
relatore Prof. Vistoli, Angelo
Parole chiave
  • deformation theory
  • fibered categories
  • formal deformations
  • obstruction theory
  • tangent functors
Data inizio appello
24/07/2009
Consultabilità
Completa
Riassunto
We give an exposition of the formal aspects of deformation theory in the language of fibered categories, instead of the more traditional one of functors. The main concepts are that of tangent space to a deformation problem, obstruction theory, versal and universal formal deformations. We include proofs of two key results: a versione of Schlessinger's Theorem in this context, and the Ran--Kawamata vanishing theorem for obstructions. We accompany this with a detailed analysis of three important cases: smooth varieties, local complete intersection subschemes and coherent sheaves.
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