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Seminar on Algebraic Geometry

 
November 2002
11. 11. Josef Schicho Del Pezzo surfaces, cubic surfaces
rational surface, parametric genus, linear system of curves, Castelnuovo criteria, lattice polygons
18. 11. Josef Schicho Del Pezzo surfaces, cubic surfaces 2
lines on Del Pezzo surfaces, Cayley-Bachamat theorem, weighted projective space,
problems (Diophantine questions, real problems, find: a special curve, a point, parametrization)
25. 11. Christian Vogt Puiseux series, Newton polygon
 
December 2002
2. 12. Christian Vogt Puiseux series, Newton polygon 2
9. 12. Ibolya Szilagyi The theorem of Hilbert-Burch
complex, exact complex, free-resolution, Hilbert-Burch theorem
 
January 2003
6.1. Josef Schicho Complexity of resolution of singularities of curves
motivation, known results, available methods, precise question
13.1. Gábor Bodnár Normalization of affine domains
 
March 2003
11.3. Janka Pílniková Solving quadratic forms of 3 variables over rationals
necessary and sufficient condition of solvability, Legendre theorem, Magma demo
27.3. Josef Schicho Toric theory of adjoints
toric surface, embedding dimension, degree, rational genus, Pick's theorem, birational map, examples
 
April 2003
3.4. Janka Pílniková Introduction to p-adic numbers
p-adic numbers, Hasse principle, examples
 
May 2003
8.5. Josef Schicho Adjoints
graded coordinate ring, coordinate-free decription of a projective variety, regular function,
isomorphism, rational function
15.5. Gábor Bodnár Introduction to understand Mega talk
concept of gluing, blowing-up, resolution of singularities
22.5. Gábor Bodnár MEGA talk
localization, blowing-up, resolution of singularities
 
June 2003
5.6. Josef Schicho Adjoints
12.6. Josef Schicho Regular diff. forms on curves, canonical maps for curves
26.6. Josef Schicho Picard group of a variety
divisor, effective divisor, principle divisor, prime divisor, canonical divisor, linear system of divisors