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

By David Eisenbud,Joe Harris

This publication can shape the root of a moment path in algebraic geometry. As motivation, it takes concrete questions from enumerative geometry and intersection conception, and gives instinct and strategy, in order that the coed develops the facility to unravel geometric difficulties. The authors clarify key rules, together with rational equivalence, Chow jewelry, Schubert calculus and Chern sessions, and readers will get pleasure from the ample examples, many supplied as routines with strategies on hand on-line. Intersection is worried with the enumeration of suggestions of platforms of polynomial equations in different 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 basic conics used to be an immense landmark, and was once the muse at the back of the name of this booklet. Such computations have been motivation for Poincaré's improvement of topology, and for plenty of next theories, in order that intersection conception is now a critical subject of contemporary mathematics.

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