Computing the equations of a variety

Authors:
Michela Brundu and Mike Stillman

Journal:
Trans. Amer. Math. Soc. **337** (1993), 677-690

MSC:
Primary 13P10; Secondary 13A30, 13D45, 14B15

DOI:
https://doi.org/10.1090/S0002-9947-1993-1091704-X

MathSciNet review:
1091704

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a projective variety or subscheme, and let be an invertible sheaf on . A set of global sections of determines a map from a Zariski open subset of to . The purpose of this paper is to find, given and , the homogeneous ideal defining the image in of this rational map. We present algorithms to compute the ideal of the image. These algorithms can be implemented using only the computation of Gröbner bases and syzygies, and they have been implemented in our computer algebra system Macaulay. Our methods generalize to include the case when is an arbitrary projective scheme and is generically invertible.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1993-1091704-X

Keywords:
Line bundle,
invertible sheaf,
rational map,
computing,
Gröbner bases,
symmetric algebra,
local cohomology

Article copyright:
© Copyright 1993
American Mathematical Society