Lefschetz properties and the Veronese construction

Martina Kubitzke, Satoshi Murai

Research output: Contribution to journalArticle

Abstract

In this paper, we investigate Lefschetz properties of Veronese subalgebras. We show that, for a sufficiently large r, the rth Veronese subalgebra of a Cohen-Macaulay standard graded K-algebra has properties similar to the weak and strong Lefschetz properties, which we call the 'quasi-weak' and 'almost strong' Lefschetz properties. By using this result, we obtain new results on h- and g-polynomials of Veronese subalgebras.

Original languageEnglish
Pages (from-to)1043-1053
Number of pages11
JournalMathematical Research Letters
Volume19
Issue number5
DOIs
Publication statusPublished - 2012 Jan 1
Externally publishedYes

Fingerprint

Subalgebra
Cohen-Macaulay
Algebra
Polynomial
Standards

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Lefschetz properties and the Veronese construction. / Kubitzke, Martina; Murai, Satoshi.

In: Mathematical Research Letters, Vol. 19, No. 5, 01.01.2012, p. 1043-1053.

Research output: Contribution to journalArticle

Kubitzke, Martina ; Murai, Satoshi. / Lefschetz properties and the Veronese construction. In: Mathematical Research Letters. 2012 ; Vol. 19, No. 5. pp. 1043-1053.
@article{c8fa07632d674f7389671a8404fea980,
title = "Lefschetz properties and the Veronese construction",
abstract = "In this paper, we investigate Lefschetz properties of Veronese subalgebras. We show that, for a sufficiently large r, the rth Veronese subalgebra of a Cohen-Macaulay standard graded K-algebra has properties similar to the weak and strong Lefschetz properties, which we call the 'quasi-weak' and 'almost strong' Lefschetz properties. By using this result, we obtain new results on h- and g-polynomials of Veronese subalgebras.",
author = "Martina Kubitzke and Satoshi Murai",
year = "2012",
month = "1",
day = "1",
doi = "10.4310/MRL.2012.v19.n5.a7",
language = "English",
volume = "19",
pages = "1043--1053",
journal = "Mathematical Research Letters",
issn = "1073-2780",
publisher = "International Press of Boston, Inc.",
number = "5",

}

TY - JOUR

T1 - Lefschetz properties and the Veronese construction

AU - Kubitzke, Martina

AU - Murai, Satoshi

PY - 2012/1/1

Y1 - 2012/1/1

N2 - In this paper, we investigate Lefschetz properties of Veronese subalgebras. We show that, for a sufficiently large r, the rth Veronese subalgebra of a Cohen-Macaulay standard graded K-algebra has properties similar to the weak and strong Lefschetz properties, which we call the 'quasi-weak' and 'almost strong' Lefschetz properties. By using this result, we obtain new results on h- and g-polynomials of Veronese subalgebras.

AB - In this paper, we investigate Lefschetz properties of Veronese subalgebras. We show that, for a sufficiently large r, the rth Veronese subalgebra of a Cohen-Macaulay standard graded K-algebra has properties similar to the weak and strong Lefschetz properties, which we call the 'quasi-weak' and 'almost strong' Lefschetz properties. By using this result, we obtain new results on h- and g-polynomials of Veronese subalgebras.

UR - http://www.scopus.com/inward/record.url?scp=84876894623&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84876894623&partnerID=8YFLogxK

U2 - 10.4310/MRL.2012.v19.n5.a7

DO - 10.4310/MRL.2012.v19.n5.a7

M3 - Article

VL - 19

SP - 1043

EP - 1053

JO - Mathematical Research Letters

JF - Mathematical Research Letters

SN - 1073-2780

IS - 5

ER -