Abstract
Solving a system of polynomial equations is a ubiquitous problem in the applications of mathematics. Until recently, it has been hopeless to find explicit solutions to such systems, and mathematics has instead developed deep and powerful theories about the solutions to polynomial equations. Enumerative Geometry is concerned with counting the number of solutions when the polynomials come from a geometric situation and Intersection Theory gives methods to accomplish the enumeration.
Supported in part by NSF grant DMS-0070494.
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Sottile, F. (2002). From Enumerative Geometry to Solving Systems of Polynomial Equations. In: Eisenbud, D., Stillman, M., Grayson, D.R., Sturmfels, B. (eds) Computations in Algebraic Geometry with Macaulay 2. Algorithms and Computation in Mathematics, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04851-1_6
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