Standard bases and geometric invariant theoryI. Initial ideals and state polytopes

Bayer, David; Morrison, Ian

doi:10.1016/s0747-7171(88)80043-9

Cited by 53 publications

(44 citation statements)

References 7 publications

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“…, x m . See [Bayer and Morrison 1988;Mora and Robbiano 1988] for the original work on the Gröbner fan, and [Sturmfels 1996;Maclagan and Thomas 2007] for expositions. When we want to refer to both fans simultaneously we use the notation .…”

Section: Amentioning

confidence: 99%

Equations for Chow and Hilbert quotients

Gibney¹,

Maclagan

2010

ANT

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We give explicit equations for the Chow and Hilbert quotients of a projective scheme X by the action of an algebraic torus T in an auxiliary toric variety. As a consequence we provide geometric invariant theory descriptions of these canonical quotients, and obtain other GIT quotients of X by variation of GIT quotient. We apply these results to find equations for the moduli space M 0,n of stable genus-zero n-pointed curves as a subvariety of a smooth toric variety defined via tropical methods.

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Section: Amentioning

confidence: 99%

Equations for Chow and Hilbert quotients

Gibney¹,

Maclagan

2010

ANT

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“…Indeed, Lemma 3.3 and Corollary 3.4 of [2] deal with the generic case of our Proposition 1. We write the details here in a form convenient for our application.…”

Section: A Gröbner Basis Algorithm For Computing the Hilbert-mumford mentioning

confidence: 96%

“…This algorithm seems to have been known to certain experts (see [1] and [2]). Indeed, Lemma 3.3 and Corollary 3.4 of [2] deal with the generic case of our Proposition 1.…”

Section: A Gröbner Basis Algorithm For Computing the Hilbert-mumford mentioning

confidence: 99%

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Stability Computation via Grobner Basis

Hassett¹,

Hyeon²,

Lee³

2010

Journal of the Korean Mathematical Society

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“…The initial ideal in ≺ (I) of I with respect to ≺ is the monomial ideal generated by the initial terms of all polynomials in I. The following theorem appears in [2] and [5], and is well known. Given an N d grading on S, we can define the Hilbert series of a homogeneous ideal by Proof.…”

Section: Corollariesmentioning

confidence: 99%