MAT 614 Syllabus Intersection Theory Fall 2014

What follows is a tentative syllabus. The pace of these topics (as well as any additional topics to be covered) will be finalized in the first weeks of the semester.

• Cycles, Rational Equivalence and Chow Groups.
• Basic Properties. Proper Pushforward. Flat Pullback.
• Divisor Classes. Projective Bundles, Segre Classes and Chern Classes.
• Chow Groups of Grassmannians, Flag Varieties and Flag Bundles. The Thom-Porteous Formula.
• Deformation to the Normal Cone.
• Intersection Products. Refined Gysin Homomorphisms.
• Intersection Multiplicities. Computational Approaches.
• The Grothendieck-Riemann-Roch Formula.
• Applications.

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