Introduction to algebraic curves and abelian varieties

Mathematics 258y
Course number 4767


Course Description
 This course will give an introduction to the study of algebraic curves and abelian varieties.  One focus will be on the relation between the geometry of a curve and its associated Jacobian variety.  To this end, we will study the theory of linear series on a fixed curve, and in particular the varieties parameterizing these linear series.  We will also give a brief introduction to the study of abelian varieties in order to consider the Torelli theorem, the Schottky problem, and more generally, the geometry of theta divisors.  A prerequisite for the course is a one year introduction to algebraic geometry.
Schedule Tuesdays and Thursdays, 11:30AM-1:00PM, Science Center 112
(Harvard Academic Calendar)
Instructor
 Sebastian Casalaina-Martin
Science Center 334
casa@math.harvard.edu
Office Hours
 Mondays        11:00AM-12:00PM
Wednesdays   9:30AM-10:30AM
TA
 Maksym Fedorchuk
Texts
  1. E. Arbarello, M. Cornalba, P. Griffiths,  and J. Harris,  Geometry of algebraic curves. Vol. I. Grundlehren der Mathematischen Wissenschaften, 267. Springer-Verlag, New York, 1985. ISBN: 0-387-90997-4.
  2. C. Birkenhake and H. Lange, Complex abelian varieties. Second edition. Grundlehren der Mathematischen Wissenschaften, 302. Springer-Verlag, Berlin, 2004.  ISBN: 3-540-20488-1.
  3. P. Griffiths and J. Harris, Principles of algebraic geometry. Reprint of the 1978 original. Wiley Classics Library. John Wiley & Sons, Inc., New York, 1994.  ISBN: 0-471-05059-8 14-01.
  4. D. Mumford, Abelian Varieties, Tata Institute of Fundamental Research Studies in Mathematics, No. 5 Published for the Tata Institute of Fundamental Research, Bombay; Oxford University Press, London 1970.
Homework and Section
 There will be weekly homework assignments, posted on this page.  
A weekly section will be led by the TA Maksym Fedorchuk  Thursdays 4:00-5:00, Science Center 232.
Syllabus
 This syllabus is a rough guide to topics we will cover.