MAT 670 Topics in advanced complex analysis
Complex Abelian varieties
Fall 2009
MEETING TIMES.
Tu+Th 11:20am-12:40am, Earth&Space 177, Instructor: Mark
De Cataldo.
PREREQUISITES and COREQUISITES:
The prerequisites for this course are:
Core courses in complex analysis, algebra, geometry and topology,
or permission of the
instructor.
SYLLABUS.
In complex geometry, Abelian varieties are quotients of complex Euclidean space by full
lattices,
i.e. complex tori, which can be embedded into some projective space, not all can.
While these varieties are all diffeomorphic to each other,
their complex structure varies in a very interesting way. Their geometry is far from
trivial and many fundamental general questions
remain open even for these varieties, e.g. the Hodge Conjecture. Their study, in
classical and in present times, has always been
rewarding. In this course, I will discuss some of the topological, geometric and
algebraic aspects
of these varieties. I will cover selected topics from C. Birkenhake, H. Lange's book:
Complex Abelian Varieties
(2nd ed.; quite different from the 1st ed.). I will not assume knowledge of algebraic
geometry and will
discuss background facts and notions when needed.
First day of class: TU SEP 1. Last day of class: TH DEC 10. No
class on TU SEP 29 (follows MO schedule) and TH NOV 26 (TKSgiving); 28 lectures.
SPECIAL NEEDS:
If you have a physical, psychological, medical, or learning disability
that may impact your course work, please contact Disability Support
Services at (631) 632-6748 or
http://studentaffairs.stonybrook.edu/dss/. They will determine with you
what accommodations are necessary and appropriate. All information and
documentation is confidential. Students who require assistance during
emergency evacuation are encouraged to discuss their needs with their
professors and Disability Support Services. For procedures and
information go to the following website:
http://www.sunysb.edu/ehs/fire/disabilities.shtml
Mark
Andrea
de Cataldo's homepage.
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