2018 - 2019 | |||||||||||||||||||||||||||||
0366-5070 | Algebraic Geometry 2 | ||||||||||||||||||||||||||||
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FACULTY OF EXACT SCIENCES | |||||||||||||||||||||||||||||
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Sheaves theory: sheaves and sheafification. Quasi-coherent sheaves. Locally free sheaves. Differentials. Line bundles on curves. The Riemann-Hurwitz formula. The Riemann-Roch theorem.
Cohomology of sheaves: Definitions. The long exact cohomology sequence. The Riemann-Roch theorem revisited. The cohomology of line bundles on projective spaces. Independence of the affine cover.
Intersection theory: Chow groups. Proper push-forward of cycles. Weil and Cartier divisors. Intersection with Cartier divisors.
Chern classes: Projective bundles. Segre and Chern classes of projective bundles. Properties of Chern classes. Hirzebruch-Riemann-Roch theorem.