Vertiefungsmodul = Forschungsmodul => Seminar "Algebra/Algebraische Geometrie" (Winter 2022/23, Mo 16:15-17:45 Arnim 3, Raum 115) http://www.math.fu-berlin.de/altmann/LEHRE/xx22_WS_Algeom_FS/agSem_WWW --------------------------------------------------------------------------- REFERENCES: [ADHL] Arzhantsev, Derental, Hausen, Laface: Cox Rings Cambridge Univ. Press, 2015 [Dol] Dolgachev: Lectures on Invariant Theory, LMS Lecture Notes Series 296, Cambridge Univ. Press, 2003 [GL] Gonzales, Laface: Finite generation of Cox rings arXiv:2209.15633v1 [math.AG] = 2209.15633_LafaceCox.pdf Section 2 in versHom = coneSetup.pdf --------------------------------------------------------------------------- SUBJECTS of TALKS: 1) Graded rings, Veronese sub-algebras associated to sub-monoids [ADHL] (1.1), [GL] sect 1, p.2/3 2) Quasitori and good + categorical quotients [ADHL] (1.2), [Dol] (6.1) 3) Actions of finite groups or of Sl(V) [Dol] (3.1) + (3.2) 4) Reductive algebraic groups Glance through [Dol] (3.3) (most of it is known from class; Spm=Spec) [Dol] (3.4), [Dol] (6.2) 5) (Sheaves of) divisorial algebras [ADHL] (1.3) 6) Cox sheaves and rings [ADHL] (1.4), [GL] sect 1, p.4/5 7) Algebraic properties of the Cox ring [ADHL] (1.5) - in particular Theorem 1.5.3.7 = Cl(X)-factoriality of Cox(X) 8) Geometry of the Cox sheaf [ADHL] (1.6), [GL] sect 2, p.5/6 9) Cox rings of toric varieties Glance through [ADHL] (2.1.1) + (2.1.2) [ADHL] (2.1.3) + (2.1.4) 10) Gale duality and GKZ decomposition [ADHL] (2.2), coneSetup.pdf 11) Good toric quotients [ADHL] (2.3) 12) GIT for quasitorus actions on affine varieties [ADHL] (3.1) --------------------------------------------------------------------------- We will start on Monday, 10/17 at 4:15 pm for a first meeting - mainly to establish first contact and to distribute talks. Whenever somebody is interested in preparing a talk of a special subject, please write me or tell me during the first session. I will then, as soon as possible, update the list below. SCHEDULE of TALKS: Mo, 17.10.: Klaus Altmann: Introduction + distribution of talks Mo, 24.10.: Klaus Altmann: Overview of toric varieties Mo, 31.10.: Ziwei Zhang: (1) Graded rings, Veronese sub-algebras Mo, 7.11.: [14-18: Festkolloquium Aigner80] Mo, 14.11.: Ziwei Zhang: (1), Part 2 Mo, 21.11.: Nicolas Beck: (2) Quasitori and quotients Mo, 28.11.: Nicolas Beck: (2), Part 2 Mo, 5.12.: Hang Chen: (3/4) Reductive algebraic groups + quotients Mo, 12.12.: Hang Chen: (3/4), Part 2 Mo, 2.1.: Wennan Zhang: (5) (Sheaves of) divisorial algebras Mo, 9.1.: Wennan Zhang: (5), Part 2 Mo, 16.1.: Wennan Zhang: (5), Part 3 Mo, 23.1.: Kyle Huang: (6) Cox sheaves and rings Mo, 30.1.: Ibrahim El Agami: (7) Algebraic properties of the Cox ring Mo, 6.2.: Ibrahim El Agami: (7), Part 2 Mo, 13.2.: / Jaquim Ribeiro: (3/4) Actions of finite groups and Sl(V)