[Liste-CICMA] Mini course in algebraic geometry by Ernesto Mistretta

Guillermo Martinez-Zalce martinez at crm.umontreal.ca
Mon Jan 19 09:44:03 EST 2015

Special Mini-course in Algebraic Geometry

Dear Colleagues and Students,

Professor Ernesto Mistretta (University of Padova) is visiting Montreal and will be giving a series of lectures in algebraic geometry. His plan is to cover, as much as there is interest, the following:

A) Vector bundles:
- definitions, morphisms, sections;
- equivalence vector bundles locally free sheaves;
- globally generated vector bundles (+ base locus of a line bundle).

B) Line bundles:
- Pic(X), Car(X), Div(X) + relations;
- exponential sequence + numerical equivalence;
- NS(X), N^1(X) over integer rational or real coefficients.
(parenthesis if time) - Chow groups, singular varieties A^p (X) and A_p(X);

C) Numerical properties:
- ample, nef are numerical properties;
- being globally generated (or semiample) is NOT a num. property;
- even effective is NOT a num. property;
- big is anumerical property.
(if time) - Iitaka fibration + ideas from birational geometry.

D) Asymptotic base loci and cones in N^1:
- the ample cone and the nef cone in N^1;
- the big cone and the nef cone in N^1;
- their dual cones in the space of 1-cycles;
- how to generalize to higher codimensional cycles? To vector bundles?
To Chern classes?

The first three meetings are 
Friday January 23, 9:30 - 11:30 at McGill, room 1205
Monday January 26, 12:30 - 14:30 at McGill, room 1214
Friday, January 30, 9:30 - 11:30 at McGill, room 1205

Additional lectures will be scheduled if there is sufficient interest. 

All are welcome. 

-- Eyal Goren.

Guillermo Martinez-Zalce
Responsable des laboratoires
Centre de recherches mathématiques
Université de Montréal
Case postale 6128, Succursale centre-ville
Montréal (Québec)
H3C 3J7
tel: (514) 343-7574
      (514) 398-3826 (mercredis)

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