Topics in Algebraic Geometry: Algebraic Surfaces

cubic surface with rational double points

An example of a cubic surface with singularities. Eight lines on the cubic surface are shown. On a nonsingular cubic surface, there are always 27 lines. (Image courtesy of Dr. Oliver Labs and Prof. Duco van Straten,


MIT Course Number


As Taught In

Spring 2008



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Course Features

Course Description

The main aims of this seminar will be to go over the classification of surfaces (Enriques-Castelnuovo for characteristic zero, Bombieri-Mumford for characteristic p), while working out plenty of examples, and treating their geometry and arithmetic as far as possible.

Other OCW Versions

This is a graduate-level course in Algebraic Geometry. The content varies year to year, according to the interests of the instructor and the students.

Abhinav Kumar. 18.727 Topics in Algebraic Geometry: Algebraic Surfaces, Spring 2008. (Massachusetts Institute of Technology: MIT OpenCourseWare), (Accessed). License: Creative Commons BY-NC-SA

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