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Syzygies, finite length modules, and random curves. (English) Zbl 1359.13029
Eisenbud, David (ed.) et al., Commutative algebra and noncommutative algebraic geometry. Volume I: Expository articles. Cambridge: Cambridge University Press (ISBN 978-1-107-06562-8/hbk). Mathematical Sciences Research Institute Publications 67, 25-52 (2015).
Summary: We apply the theory of Gröbner bases to the computation of free resolutions over a polynomial ring, the defining equations of a canonically embedded curve, and the unirationality of the moduli space of curves of a fixed small genus.
For the entire collection see [Zbl 1333.13002].

13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
13D05 Homological dimension and commutative rings
13C40 Linkage, complete intersections and determinantal ideals
14-04 Software, source code, etc. for problems pertaining to algebraic geometry
14M20 Rational and unirational varieties
14H10 Families, moduli of curves (algebraic)
14Q05 Computational aspects of algebraic curves
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