Hilbert schemes and maximal Betti numbers over veronese rings

Vesselin Gasharov, Satoshi Murai, Irena Peeva*

*この研究の対応する著者

研究成果: Article査読

6 被引用数 (Scopus)

抄録

Macaulay's Theorem (Macaulay in Proc. Lond Math Soc 26:531-555, 1927) characterizes the Hilbert functions of graded ideals in a polynomial ring over a field. We characterize the Hilbert functions of graded ideals in a Veronese ring R (the coordinate ring of a Veronese embedding of Pr-1). We also prove that the Hilbert scheme, which parametrizes all graded ideals in R with a fixed Hilbert function, is connected; this is an analogue of Hartshorne's Theorem (Hartshorne in Math. IHES 29:5-48, 1966) that Hilbert schemes over a polynomial ring are connected. Furthermore, we prove that each lex ideal in R has the greatest Betti numbers among all graded ideals with the same Hilbert function.

本文言語English
ページ(範囲)155-172
ページ数18
ジャーナルMathematische Zeitschrift
267
1
DOI
出版ステータスPublished - 2011 2月 1
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

フィンガープリント

「Hilbert schemes and maximal Betti numbers over veronese rings」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル