Complex Algebraic Surfaces Class 6

Complex Algebraic Surfaces Class 18

It makes use of the last general construction commonly used in the theory of algebraic surfaces, the Albanese variety. After seeing this, I think you’ll be fully equipped to read much of the literature on surfaces in the algebraic category. On Friday, the last day of class, I’ll then sketch the rest of the classification of algebraic surfaces. In particular, you’re familiar with all the ingredi...

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...

Complex Algebraic Surfaces Class 16

Complex Algebraic Surfaces Class 17

Curve Complexes of Non-orientable Surfaces

We explore non-orientable surfaces and their associated curve complexes. Studying the combinatorics modeled by the curve complex of a surface helps elucidate the algebraic properties of the mapping class group of the surface. We begin by studying geometric properties of the curve complexes of non-orientable surfaces and the geometric properties of natural sub-complexes of the curve complex. Fin...