Advanced Training in Mathematics Schools

(Supported by National Board for Higher Mathematics)

Advanced Instructional School on Schemes & Cohomology

28 June - 16 July, 2010

  Advanced Instructional School on Schemes & Cohomology is being organised at KSOM, Kozhikode in the month of June - July 2010.

                                                                                       

Speakers

1 Suresh Naik
2 D. S. Nagaraj
3 TEV Balaji
4 A. J. Parameswaran
5 K. N. Raghavan
6 V. Balaji
7 Vivek Mallik

Syllabus

 The AIS will be directed towards making young researchers in India familiar with the developments in Algebraic Geometry, with special emphasis on Grothendieck's programme. The three week programme is primarily aimed at early researchers in this field to become familiar and users of the tools and techniques in this subject.


Topics
Sheaves, schemes, elementary properties of schemes, morphisms, invertible sheaves and bundles, differ-entials, valuative criterion, Bertini's theorems, Lefschetz hy-perplane section theorem. Derived functors, cohomology of sheaves, Cech cohomology, Cohomology of projective space,Serre duality, semicontinuity theorems , Zariski's main theorem and Zariski's connectedness theorem, Fulton-Lazarsfeld con-nectedness theorem. Applications to Brill-Noether theory.