This booklet can shape the foundation of a moment path in algebraic geometry. As motivation, it takes concrete questions from enumerative geometry and intersection idea, and gives instinct and method, in order that the scholar develops the facility to resolve geometric difficulties. The authors clarify key rules, together with rational equivalence, Chow jewelry, Schubert calculus and Chern sessions, and readers will delight in the considerable examples, many supplied as workouts with strategies to be had on-line. Intersection is anxious with the enumeration of ideas of platforms 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 aircraft curves tangent to 5 given normal conics was once an immense landmark, and was once the foundation in 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 relevant subject of recent arithmetic.

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