| preface list of contributors part i introducing macaulay 2 ideals, varieties and macaulay 2 bernd sturmfels 1 a curve in affine three-space 2 intersecting our curve with a surface 3 changing the ambient polynomial ring 4 monomials under the staircase 5 pennies, nickels, dimes and quarters references projective geometry and homological algebra david eisenbud 1 the twisted cubic 2 the cotangent bundle of i?3 3 the cotangent bundle of a projective variety 4 intersections by serre's method 5 a mystery variety in ]?3 appendix a. how the "mystery variety" was made references . data types, fhlnctions, and programming daniel r. grayson and michael e. stillman 1 basic data types 2 control structures 3 input and output 4 hash tables 5 methods 6 pointers to the source code references teaching the geometry of schemes gregory g. smith and bernd sturmfels 1 distinguished open sets 2 irreducibility 3 singular point 4 fields of definition 5 multiplicity 6 flat families 7 bezout's theorem 8 constructing blow-ups 9 a classic blow-up 10 fano schemes references part ii mathematical computations monomial ideals serkan hosaten and gregory g. smith 1 the basics of monomial ideals 2 primary decomposition 3 standard pairs 4 generic initial ideals 5 the chain property references from enumerative geometry to solving systems of polynomial equations frank sottile 1 introduction 2 solving systems of polynomials 3 some enumerative geometry 4 schubert calculus 5 the 12 lines: reprise references resolutions and cohomology over complete intersections luchezar l. avramov and daniel r. grayson 1 matrix factorizations 2 graded algebras 3 universm homotopies 4 cohomology operators 5 computation of ext modules 6 invariants of modules 7 invariants of pairs of modules appendix a. gradings references algorithms for the toric hilbert scheme sheaf algorithms using the exterior algebra needles in a haystack:special varieties via small fields d-modules and cohomology of varieties index |
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