Local Equations for the Toric Hilbert Scheme

نویسندگان

  • Irena Peeva
  • Mike Stillman
چکیده

We obtain local equations for the toric Hilbert scheme, which parametrizes all ideals with the same multigraded Hilbert function as a given toric ideal. We also prove a conjecture of Sturmfels’ providing a criterion for an ideal to have such a Hilbert function.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Equations for Chow and Hilbert Quotients

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 GIT 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 M0,n of stable genus zero n-pointed cu...

متن کامل

Multigraded Hilbert Schemes

We introduce the multigraded Hilbert scheme, which parametrizes all homogeneous ideals with fixed Hilbert function in a polynomial ring that is graded by any abelian group. Our construction is widely applicable, it provides explicit equations, and it allows us to prove a range of new results, including Bayer’s conjecture on equations defining Grothendieck’s classical Hilbert scheme and the cons...

متن کامل

Combinatorics of the Toric Hilbert Scheme

The toric Hilbert scheme is a parameter space for all ideals with the same multi-graded Hilbert function as a given toric ideal. Unlike the classical Hilbert scheme, it is unknown whether toric Hilbert schemes are connected. We construct a graph on all the monomial ideals on the scheme, called the flip graph, and prove that the toric Hilbert scheme is connected if and only if the flip graph is ...

متن کامل

Combinatorics of the Toric Hilbert Scheme Diane Maclagan and Rekha R. Thomas

The toric Hilbert scheme is a parameter space for all ideals with the same multi-graded Hilbert function as a given toric ideal. Unlike the classical Hilbert scheme, it is unknown whether toric Hilbert schemes are connected. We construct a graph on all the monomial ideals on the scheme, called the flip graph, and prove that the toric Hilbert scheme is connected if and only if the flip graph is ...

متن کامل

The Toric Hilbert Scheme of a Rank Two Lattice Is Smooth and Irreducible Diane Maclagan and Rekha R. Thomas

The toric Hilbert scheme of a lattice L ⊆ Z is the multigraded Hilbert scheme parameterizing all ideals in k[x1, . . . , xn] with Hilbert function value one for every g in the grading monoid G = N/L. In this paper we show that if L is twodimensional, then the toric Hilbert scheme of L is smooth and irreducible. This result is false for lattices of dimension three and higher as the toric Hilbert...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1999