NDLI: Toric Initial Ideals of Δ-Normal Configurations: Cohen-Macaulayness and Degree Bounds

Content Provider	Springer Nature Link
Author	O’Shea, Edwin Thomas, Rekha R.
Copyright Year	2005
Abstract	A normal (respectively, graded normal) vector configuration $${\cal A}$$ defines the toric ideal $${I}_{\cal A}$$ of a normal (respectively, projectively normal) toric variety. These ideals are Cohen-Macaulay, and when $${\cal A}$$ is normal and graded, $${I}_{\cal A}$$ is generated in degree at most the dimension of $${I}_{\cal A}$$ . Based on this, Sturmfels asked if these properties extend to initial ideals—when $${\cal A}$$ is normal, is there an initial ideal of $${I}_{\cal A}$$ that is Cohen-Macaulay, and when $${\cal A}$$ is normal and graded, does $${I}_{\cal A}$$ have a Gröbner basis generated in degree at most dim( $${I}_{\cal A}$$ ) ? In this paper, we answer both questions positively for Δ-normal configurations. These are normal configurations that admit a regular triangulation Δ with the property that the subconfiguration in each cell of the triangulation is again normal. Such configurations properly contain among them all vector configurations that admit a regular unimodular triangulation. We construct non-trivial families of both Δ-normal and non-Δ-normal configurations.
Starting Page	247
Ending Page	268
Page Count	22
File Format	PDF
ISSN	09259899
Journal	Journal of Algebraic Combinatorics
Volume Number	21
Issue Number	3
e-ISSN	15729192
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2005-01-01
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	toric ideals triangulations Hilbert bases Gröbner bases Computer Science Group Theory and Generalizations Order, Lattices, Ordered Algebraic Structures Combinatorics Convex and Discrete Geometry
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Algebra and Number Theory

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