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THE HILBERT SCHEME
"... Many important moduli spaces can be constructed as quotients of the Hilbert scheme by a group action. For example, to construct the moduli space of smooth curves of genus g ≥ 2, we can first embed all smooth curves of genus g in Pn(2g−2)−g by a sufficiently large multiple of their canonical bundle K ..."
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Many important moduli spaces can be constructed as quotients of the Hilbert scheme by a group action. For example, to construct the moduli space of smooth curves of genus g ≥ 2, we can first embed all smooth curves of genus g in Pn(2g−2)−g by a sufficiently large multiple of their canonical bundle
Multigraded Hilbert schemes
 J. Algebraic Geom
"... 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, includ ..."
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Cited by 63 (3 self)
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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
Combinatorics Of The Toric Hilbert Scheme
 DISCRETE COMPUT. GEOM
, 2002
"... The toric Hilbert scheme is a parameter space for all ideals with the same multigraded 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 t ..."
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Cited by 8 (5 self)
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The toric Hilbert scheme is a parameter space for all ideals with the same multigraded 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
Toric Hilbert schemes
 Duke Math. J
, 1999
"... Abstract: We introduce and study the toric Hilbert scheme which parametrizes all ideals with the same multigraded Hilbert function as a given toric ideal. 1. ..."
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Cited by 26 (3 self)
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Abstract: We introduce and study the toric Hilbert scheme which parametrizes all ideals with the same multigraded Hilbert function as a given toric ideal. 1.
The geometry of the parabolic Hilbert schemes
, 2002
"... Let X be a smooth projective surface and D be a smooth divisor over an algebraically closed field k. In this paper, we discuss the moduli schemes of the ideals of points of X with parabolic structures at D. They are called parabolic Hilbert schemes. The first result is that the parabolic Hilbert sch ..."
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Cited by 1 (0 self)
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Let X be a smooth projective surface and D be a smooth divisor over an algebraically closed field k. In this paper, we discuss the moduli schemes of the ideals of points of X with parabolic structures at D. They are called parabolic Hilbert schemes. The first result is that the parabolic Hilbert
Questions of Connectedness of the Hilbert Scheme
 of Curves in P3 , Preprint
, 2001
"... Dedicated to S. Abhyankar on the occasion of his 70th birthday. We review the present state of the problem, for each degree d and genus g, is the Hilbert scheme of locally Cohen–Macaulay curves in P 3 connected? 1 ..."
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Cited by 5 (0 self)
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Dedicated to S. Abhyankar on the occasion of his 70th birthday. We review the present state of the problem, for each degree d and genus g, is the Hilbert scheme of locally Cohen–Macaulay curves in P 3 connected? 1
CONNECTEDNESS OF HILBERT SCHEMES
"... We show that the Hilbert scheme, that parametrizes all ideals with the same Hilbert function over an exterior algebra, is connected. We give a new proof of Hartshorne’s Theorem that the classical Hilbert scheme is connected. More precisely: if Q is either a polynomial ring or an exterior algebra, we ..."
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Cited by 9 (3 self)
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We show that the Hilbert scheme, that parametrizes all ideals with the same Hilbert function over an exterior algebra, is connected. We give a new proof of Hartshorne’s Theorem that the classical Hilbert scheme is connected. More precisely: if Q is either a polynomial ring or an exterior algebra
Instantons, Hilbert Schemes and Integrability
, 2001
"... We review the deformed instanton equations making connection with Hilbert schemes and integrable systems. A single U(1) instanton is shown to be antiselfdual with respect to the Burns metric. ..."
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We review the deformed instanton equations making connection with Hilbert schemes and integrable systems. A single U(1) instanton is shown to be antiselfdual with respect to the Burns metric.
Hilbert schemes of 8 points
 ALGEBRA AND NUMBER THEORY
, 2009
"... The Hilbert scheme H d n of n points in �d contains an irreducible component Rd n which generically represents n distinct points in �d. We show that when n is at most 8, the Hilbert scheme H d n is reducible if and only if n = 8 and d ≥ 4. In the simplest case of reducibility, the component R4 8 ⊂ H ..."
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Cited by 16 (3 self)
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The Hilbert scheme H d n of n points in �d contains an irreducible component Rd n which generically represents n distinct points in �d. We show that when n is at most 8, the Hilbert scheme H d n is reducible if and only if n = 8 and d ≥ 4. In the simplest case of reducibility, the component R4 8
On the tropicalization of the Hilbert scheme,
 Collect. Math.
, 2013
"... Abstract In this article we study the tropicalization of the Hilbert scheme and its suitability as a parameter space for tropical varieties. We prove that the points of the tropicalization of the Hilbert scheme have a tropical variety naturally associated to them. To prove this, we find a bound on ..."
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Cited by 4 (0 self)
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Abstract In this article we study the tropicalization of the Hilbert scheme and its suitability as a parameter space for tropical varieties. We prove that the points of the tropicalization of the Hilbert scheme have a tropical variety naturally associated to them. To prove this, we find a bound
Results 1  10
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