Smooth and irreducible multigraded Hilbert schemes

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• 作者：Diane Maclagan ; Gregory G. Smith
• 关键词：Hilbert schemes ; Multigraded rings ; Combinatorial commutative algebra
• 刊名：Advances in Mathematics
• 出版年：2010
• 出版时间：20 March 2010
• 年：2010
• 卷：223
• 期：5
• 页码：1608-1631
• 全文大小：295 K

文摘

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 , which establishes a conjecture of Haiman and Sturmfels.