Seminar "Algebra/Algebraische Geometrie" (Sommer 2017, Mo 14:15-15:45 Arnim 3, Raum 119) --------------------------------------------------------------------------- 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 --------------------------------------------------------------------------- Mo, 24.4.: Doppel-FS-seminar => Kein AG-Seminar [Ausgleich 8.5.] Mo, 8.5.: a) Patrick Da Silva: Positive Wurzeln und Wurzelbasen b) Maik Pickl: (1) Divisors and line bundles Mo, 15.5.: Maik Pickl: Part 2 Mo, 22.5.: Diana Dörner: (2) Intersection of curves and divisors Mo, 29.5.: Diana Dörner: Part 2 Mo, 12.6.: Doppel-FS-seminar => Kein AG-Seminar [Ausgleich 26.6.] Mo, 19.6.: Lena Walter/Irem Portakal: (3) Ampleness criteria + the Mori cone Mo, 26.6.: a) Lena Walter/Irem Portakal: Part 2 b) Dimitri Loutchko: (4) Mo, 3.7.: Dimitri Loutchko: Part 2 Mo, 10.7.: Dominic Bunnett: (5) OR Emmi Arwid: (6) or (7) or (8) (?) Mo, 17.7.: ---------------------------------------------------------------- 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]] ----------------------------------------------------------------