3264 and All That: A Second Course in Algebraic Geometry by David Eisenbud,Joe Harris

By David Eisenbud,Joe Harris

This e-book can shape the foundation of a moment path in algebraic geometry. As motivation, it takes concrete questions from enumerative geometry and intersection conception, and offers instinct and procedure, in order that the coed develops the power to resolve geometric difficulties. The authors clarify key rules, together with rational equivalence, Chow earrings, Schubert calculus and Chern sessions, and readers will savor the ample examples, many supplied as routines with options to be had on-line. Intersection is anxious with the enumeration of suggestions of structures of polynomial equations in numerous variables. it's been an energetic sector of arithmetic because the paintings of Leibniz. Chasles' nineteenth-century calculation that there are 3264 tender conic airplane curves tangent to 5 given common conics used to be a massive landmark, and was once the foundation at the back of the name of this ebook. Such computations have been motivation for Poincaré's improvement of topology, and for plenty of next theories, in order that intersection idea is now a significant subject of recent mathematics.

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