Titlebook: Computations in Algebraic Geometry with Macaulay 2; David Eisenbud,Michael Stillman,Bernd Sturmfels Textbook 2002 Springer-Verlag Berlin H

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Michele Brignole,David G. Benditt we develop a program that produces random curves of genus . ≤ 14. In the second part we use the program to test Green’s Conjecture on syzygies of canonical curves and compare it with the corresponding statement for Coble self-dual sets of points. In the third section we apply our techniques to produce Calabi-Yau 3-folds of degree 17 in ℙ..

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https://doi.org/10.1057/9780230509559dules over a complete intersection. The duals of these infinite projective resolutions are finitely generated differential graded modules over a graded polynomial ring, so they can be represented in the computer, and can be used to compute Ext modules simultaneously in all homological degrees. It is

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From Enumerative Geometry to Solving Systems of Polynomial Equationsicit 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.

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David Eisenbud,Michael Stillman,Bernd SturmfelsOnly textbook using Macaulay as a tool.Computational algebraic geometry presented in the optimal way by top researchers.Includes supplementary material:

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