Hilbert schemes and Betti numbers over Clements–Lindström rings
2012 ◽
Vol 148
(5)
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pp. 1337-1364
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AbstractWe show that the Hilbert scheme, that parameterizes all ideals with the same Hilbert function over a Clements–Lindström ring W, is connected. More precisely, we prove that every graded ideal is connected by a sequence of deformations to the lex-plus-powers ideal with the same Hilbert function. This is an analogue of Hartshorne’s theorem that Grothendieck’s Hilbert scheme is connected. We also prove a conjecture by Gasharov, Hibi, and Peeva that the lex ideal attains maximal Betti numbers among all graded ideals in W with a fixed Hilbert function.
2014 ◽
Vol 13
(08)
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pp. 1450056
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A Simple Proof of the Formula for the Betti Numbers of the Quasihomogeneous Hilbert Schemes: Fig. 1.
2014 ◽
Vol 2015
(13)
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pp. 4708-4715
2013 ◽
Vol 149
(3)
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pp. 481-494
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2008 ◽
Vol 36
(12)
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pp. 4704-4720
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2009 ◽
Vol 267
(1-2)
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pp. 155-172
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