Department of Mathematics
Fine Hall, Washington Road Princeton, NJ 08544-1000
Office: 605 Fine Hall
Math Department Phone: (609) 258 - 4200
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review of the paper "Prizes and productivity: how winning the
Fields medal affects scientific output"
by G. J. Borjas and K. B. Doran.
CORRECTIONS TO: Lectures on Resolutions of Singularities
corrections in PDF
The structure of algebraic varieties -- talk at the 2014 Seoul ICM
original slides, with additional comments based on the oral presentation in Seoul, in PDF
Book on Moduli of Surfaces --- ongoing project
I am writing a book on the moduli of varieties of general type,
more generally about the moduli of pairs (X,D) such that
K_X+D is ample.
I will try to keep posting the chapters as they get written.
As usual, in writing a chapter one discovers that the earlier ones
should be changed, so I will try to update them as well.
Others agreed to contribute various sections, these will
be added as they become available.
Since these are not final notes, citations, references, proofs
or even entire sections may be missing.
Any comments, corrections or suggestions are welcome.
Chapter 1: Introduction
This is mostly a review of moduli theory, with lots of examples
of what can go wrong for varieties that are not canonically polarized,
or too singular, or ...
Chapter 2: Canonical models
This is mostly a review of the theory of canonical models, with special
attention to the various important classes of singularities.
(For example, canonical, klt, dlt, rational, log canonical, Du Bois, ...)
Chapter 3: Semi log canonical pairs
This gives the construction of the higher dimensional analogs of
stable curves. Some of it is quite technical.
MAT 416: Introduction to Algebraic Geometry
Topics for student projects in
MAT 416: Homework for Algebraic Geometry
Unless otherwise indicated, the files below are postscript files.
Seminar on Moduli of Surfaces --- Summer 1994
Santa Cruz 1995
Topics in Complex Algebraic Geometry, Proceedings of the MSRI Special Year
by Herbert Clemens and János Kollár
Shafarevich Maps and Automorphic Forms, Princeton Univ. Press. by János
Rational Curves on Algebraic Varieties, Springer by János Kollár
Birational Geometry of Algebraic Varieties, by János Kollár
and Shigefumi Mori, English edition: Cambridge Univ. Press, Japanese edition:
ERGEBNISSE DER MATHEMATIK, SPRINGER: Projects should be discussed with
the Managing Editor or with the editor closest to the subject of the book.