Algebraic Geometry Notes

Applicable Algebraic Geometry

PREFACE 3 Preface These lecture notes serve as material accompanying a series of lectures given within the IMA summer school Applicable Algebraic Geometry at Texas A&M University, 2007 (organized by F. Sottile, L. Matusevich and myself). The goal of the lectures is to provide an access to some important techniques as well as to some current developments in applicable algebraic geometry, in part...

Noetherianity up to symmetry

These lecture notes for the 2013 CIME/CIRM summer school Combinatorial Algebraic Geometry deal with manifestly infinite-dimensional algebraic varieties with large symmetry groups. So large, in fact, that subvarieties stable under those symmetry groups are defined by finitely many orbits of equations—whence the title Noetherianity up to symmetry. It is not the purpose of these notes to give a sy...

SMSTC (2012/13) Geometry and Topology LECTURE NOTES 5: Surfaces in Algebraic Geometry

January 23, 2013 Frances Kirwan’s book Complex algebraic curves is an excellent introduction to complex algebraic curves (see [5]). Whenever possible I have included a page reference to the book, in the form [5]. Another beautiful book on this subject is Rick Miranda’s book Algebraic curves and Riemann surfaces (see [6]). To get a feeling what is higher-dimensional complex algebraic geometry, s...

Topological Methods in Algebraic Geometry

Preface These are live-texed lecture notes for a course taught in Cambridge during Michaelmas 2013 by Burt Totaro, on a hodgepodge of topics at the intersection of algebraic topology and algebraic geometry. An unfortunate side effect of live-texing is that it tends to introduce a lot of errors, which are solely the fault of the scribe. If you find any, please let me know at

Applying Algebraic Geometry to Surface Intersection Evaluation

Focusing on surface intersection tracing, we review the familiar numerical approach. We demonstrate that it actually applies more generally than commonly assumed in the literature. We then study how to combine it with methods from algebraic geometry in an attempt to overcome the shortcomings of purely numerical techniques. These notes provide a guide to the practicing engineer for seeing how hi...

Notes for Math 7670, Algebraic Geometry