By William Fulton

This e-book introduces the various major principles of contemporary intersection idea, strains their origins in classical geometry and sketches a couple of usual functions. It calls for little technical heritage: a lot of the fabric is on the market to graduate scholars in arithmetic. A huge survey, the publication touches on many subject matters, most significantly introducing a strong new procedure built via the writer and R. MacPherson. It was once written from the expository lectures brought on the NSF-supported CBMS convention at George Mason college, held June 27-July 1, 1983. the writer describes the development and computation of intersection items via the geometry of ordinary cones. in terms of effectively intersecting forms, this yields Samuel's intersection multiplicity; on the different severe it provides the self-intersection formulation by way of a Chern type of the conventional package; commonly it produces the surplus intersection formulation of the writer and R. MacPherson. one of the functions offered are formulation for degeneracy loci, residual intersections, and a number of element loci; dynamic interpretations of intersection items; Schubert calculus and strategies to enumerative geometry difficulties; Riemann-Roch theorems.

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