Math 612: Algebraic geometryFall 2016

Instructor: Brad DrewOffice: KAP 400CLectures: MW 10:30-11:45 in KAP 427Office hours: F 10:30-11:45 or by appointmentCourse website: http://www-bcf.usc.edu/~bdrew/612/

Course description

This course will explore the basic concepts of algebraic geometry, working in the classical languageof algebraic varieties. With emphasis on concrete examples and classical motivations, we willexamine the following fundamental topics: the Zariski topology, sheaf theory, the category ofalgebraic varieties, dimension theory, projectivity and flatness, singularities and tangent spaces,and blow-ups. Depending on audience interest, we may also address more advanced topics, such asthe Riemann-Roch theorem, or linear algebraic groups and Hilbert’s fourteenth problem.

Prerequisites: Math 510a and Math 510b

Course requirements: Homework will be assigned and collected at regular intervals.

References

[AM69] Michael F. Atiyah and Ian G. Macdonald. Introduction to commutative algebra.Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969.

[BP02] Fedor Bogomolov and Tihomir Petrov. Algebraic curves and one-dimensional fields,volume 8 of Courant Lecture Notes in Mathematics. New York University, CourantInstitute of Mathematical Sciences, New York; American Mathematical Society,Providence, RI, 2002.

[Har77] Robin Hartshorne. Algebraic Geometry. Number 52. Springer-Verlag, New York, 1977.Graduate Texts in Mathematics.

[Har95] Joe Harris. Algebraic geometry, volume 133 of Graduate Texts in Mathematics.Springer-Verlag, New York, 1995. A first course, Corrected reprint of the 1992 original.

[Mil15] James S. Milne. Algebraic Geometry.http://www.jmilne.org/math/CourseNotes/ag.html, August 2015.

[Mum99] David Mumford. The red book of varieties and schemes, volume 1358 of Lecture Notes inMathematics. Springer-Verlag, Berlin, expanded edition, 1999. Includes the Michiganlectures (1974) on curves and their Jacobians, With contributions by Enrico Arbarello.

[Sha13] Igor R. Shafarevich. Basic algebraic geometry. 1. Springer, Heidelberg, third edition, 2013.Varieties in projective space.

[Vak15] Ravi Vakil. The Rising Sea: Foundations of Algebraic Geometry.http://math.stanford.edu/~vakil/216blog/, December 2015.

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