منابع مشابه
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 کاملSmooth and irreducible multigraded Hilbert schemes
The multigraded Hilbert scheme parametrizes all homogeneous ideals in a polynomial ring graded by an abelian group with a fixed Hilbert function. We prove that any multigraded Hilbert scheme is smooth and irreducible when the polynomial ring is Z[x, y], which establishes a conjecture of Haiman and Sturmfels. © 2009 Gregory G. Smith. Published by Elsevier Inc. All rights reserved.
متن کاملThe T-Graph of a Multigraded Hilbert Scheme
The T -graph of a multigraded Hilbert scheme records the zero and one-dimensional orbits of the T = (K∗)n action on the Hilbert scheme induced from the T -action on A. It has vertices the T -fixed points, and edges the onedimensional T -orbits. We give a combinatorial necessary condition for the existence of an edge between two vertices in this graph. For the Hilbert scheme of points in the pla...
متن کاملIntersection theory on punctual Hilbert schemes and graded Hilbert schemes
The rational Chow ring A(S,Q) of the Hilbert scheme S parametrising the length n zero-dimensional subschemes of a toric surface S can be described with the help of equivariant techniques. In this paper, we explain the general method and we illustrate it through many examples. In the last section, we present results on the intersection theory of graded Hilbert schemes.
متن کاملComputable Hilbert Schemes
In this PhD thesis we propose an algorithmic approach to the study of the Hilbert scheme. Developing algorithmic methods, we also obtain general results about Hilbert schemes. In Chapter 1 we discuss the equations defining the Hilbert scheme as subscheme of a suitable Grassmannian and in Chapter 5 we determine a new set of equations of degree lower than the degree of equations known so far. In ...
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ژورنال
عنوان ژورنال: Journal of Algebraic Geometry
سال: 2004
ISSN: 1056-3911,1534-7486
DOI: 10.1090/s1056-3911-04-00373-x