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Toric degenerations of low-degree hypersurfaces

Part of: Computational aspects and applications Surfaces and higher-dimensional varieties Special varieties

Published online by Cambridge University Press:  20 April 2023

Nathan Ilten  and
Oscar Lautsch
Nathan Ilten*
Affiliation:
Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6, Canada e-mail: oscar_lautsch@sfu.ca
Oscar Lautsch
Affiliation:
Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6, Canada e-mail: oscar_lautsch@sfu.ca
*
e-mail: nilten@sfu.ca
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Abstract

We show that a sufficiently general hypersurface of degree d in $\mathbb {P}^n$ admits a toric Gröbner degeneration after linear change of coordinates if and only if $d\leq 2n-1$.

Keywords

Toric degenerationhypersurfacesKhovanskii basis

MSC classification

Primary: 13P10: Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) 14J70: Hypersurfaces 14M25: Toric varieties, Newton polyhedra
Type
Article
Information
Canadian Mathematical Bulletin , Volume 66 , Issue 4 , December 2023 , pp. 1231 - 1236
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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Footnotes

N.I. was supported by an NSERC Discovery Grant. O.L. was supported by an NSERC undergraduate student research award.

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