Seminar "Algebra/Algebraische Geometrie"
(Sommer 2017, Mo 14:15-15:45 Arnim 3, Raum 119)
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Dear participants of the AG-seminar,
since we have a double feature in the other seminar on Monday
4/24, we will start our seminar on 5/8 (there is a public holiday in
between).
To catch up, we start on May 8 with a double slot 2-4 AND 4-6.
The first part is reserved for the talk of Patrick concluding
our Lie algebra/group subject from the winter semester.
The new subject of the present semester is an introduction into the
MMP ("minimal model program") or "Mori theory". I know that some people
wanted to have deformation theory again - but we had this not too long
ago. Moreover, the MMP includes deformation arguments, too (bend&break).
If Patrick keeps it short, we can use at least some time on the double
seminar on 5/8 to recall basic notions. I have called it "Talk (0)".
The official start is then on May 15 with (1).
Now, I need volunteers for giving a talk. The easy subject (0) requires
a lot of flexibility to react spontaneously on the actual time schedule
and on the needs of the audience. Please write me if you are interested
to give a talk. And whenever you have nice toric examples in mind - please
share them with us.
Best,
Klaus
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Mo, 24.4.: Doppel-FS-seminar => Kein AG-Seminar
Mo, 8.5.: a) Patrick Da Silva: Positive Wurzeln und Wurzelbasen
b) Maik Pickl: (1) Divisors and line bundles
Mo, 15.5.: Diana DÃ¶rner: (2) Intersection of curves and divisors
Mo, 22.5.: Lena Walter/Irem Portakal: (3) Ampleness criteria + the Mori cone
Mo, 29.5.: Dimitri Loutchko: (4)
Mo, 12.6.: Dominic Bunnett: (5)
Mo, 19.6.:
Mo, 26.6.:
Mo, 3.7.:
Mo, 10.7.:
Mo, 17.7.:
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MORI-THEORY, MMP
[DeBook] O.Debarre: Higher-dimensional algebraic geometry
(Springer, Universitext)
[wwwDeb] O.Debarre: Introduction to Mori theory
(www.math.ens.fr/~debarre/M2.pdf)
[CoxTV] Cox/Little/Schenck: Toric varieties
1) Divisors and line bundles
[Ch 2, pp.11-22 in [wwwDeb], (1.4) in [DeBook]]
2) Intersection of curves and divisors
[Ch 3, pp.23-32 in [wwwDeb], (1.1)-(1.3) in [DeBook],
pp.288-290 in [CoxTV]]
3) Ampleness criteria + the Mori cone
[(4.1)-(4.4), pp.33-38 in [wwwDeb], (1.5)-(1.7) in [DeBook],
pp.291-296 in [CoxTV]]
4) Riemann-Roch and surfaces
[(4.5)-(4.6), pp.38-41 in [wwwDeb], (1.5)-(1.7) in [DeBook],
Ch 5, pp.45-58 in [wwwDeb]]
5) Exceptional loci
[(1.10)-(1.11) in [DeBook]]
6) Parametrizing morphisms
[Ch 6, pp.59-66 in [wwwDeb], Ch 2, pp.37-54 in [DeBook]]
7) Bend-and-Break lemmas
[Ch 7, pp.67-76 in [wwwDeb], (3.1)-(3.4) in [DeBook]]
8) Contractions and MMP
[Ch 8, pp.77-94 in [wwwDeb], Ch 6, pp.143-166 in [DeBook],
Ch 15 of [CoxTV]]
9) Varieties with many rational curves
[Ch 9, pp.95-112 in [wwwDeb], Ch 4, pp.85-110 in [DeBook]]
10) Singularities (to be divided into several talks)
[Ch 7, pp.167-220 in [DeBook]]
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