Informazioni di Geometria Algebrica

Dipartimento: Scienze Matematiche, Fisiche E Naturali
Settore Ministeriale: MAT/03
Codice di verbalizzazione: 8065716
Metodi di insegnamento: Frontale
Metodi di valutazione: Orale
Prerequisiti: The courses of the Laurea Triennale in Mathematics of The University of Roma, Tor Vergata
Obiettivi: The course is an introduction to algebraic geometry based on Shafarevich��s book. The contents are the following. Affine and quasi-affine varieties. Projective and quasi-projective varieties. Rational and birational maps. Dimension. The local ring at at a point. Zariski tangent space. Non-singularity, UFD property and divisors. Normal varieties and normalization. Divisors, linear equivalence and linear systems. Regular and rational differential forms. Canonical divisors. Riemann-Roch for curves. Algebraic surfaces. Intersection number. Bezout��s theorem. Genus of curves an surfaces. Resolving the indetermination locus of a morphism. Abstract varieties and schemes. Sheaves of modules. Locally free sheaves vs vector bundles. Cohomology of sheaves. Complex algebraic varieties. Riemann surfaces. Divisors and meromorphic functions. Uniformization of complex algebraic curves. Universal cover. Curves of parabolic, elliptic and hyperbolic type.

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