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Singularities and radical initial ideals

Singularities and radical initial ideals What kind of reduced monomial schemes can be obtained as a Gröbner degeneration of a smooth projective variety? Our conjectured answer is: only Stanley–Reisner schemes associated to acyclic Cohen–Macaulay simplicial complexes. This would imply, in particular, that only curves of genus zero have such a degeneration. We prove this conjecture for degrevlex orders, for elliptic curves over totally real number fields, for boundaries of cross‐polytopes, and for leafless graphs. We discuss consequences for rational and F‐rational singularities of algebras with straightening laws. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

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References (36)

Publisher
Wiley
Copyright
© 2020 London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms.12358
Publisher site
See Article on Publisher Site

Abstract

What kind of reduced monomial schemes can be obtained as a Gröbner degeneration of a smooth projective variety? Our conjectured answer is: only Stanley–Reisner schemes associated to acyclic Cohen–Macaulay simplicial complexes. This would imply, in particular, that only curves of genus zero have such a degeneration. We prove this conjecture for degrevlex orders, for elliptic curves over totally real number fields, for boundaries of cross‐polytopes, and for leafless graphs. We discuss consequences for rational and F‐rational singularities of algebras with straightening laws.

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Aug 1, 2020

Keywords: ; ; ; ; ;

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