On multisecants and the Green-Lazarsfeld index of projective varieties

Wanseok Lee; Euisung Park; Youngho Woo

doi:10.1007/s00013-011-0270-1

On multisecants and the Green-Lazarsfeld index of projective varieties

Wanseok Lee, Euisung Park, Youngho Woo

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

It is well known that a nondegenerate projective subvariety X ⊂ ℙ^r of degree d and codimension c > 1 has minimal degree (i.e., d = c + 1) if and only if index(X) ≥ c if and only if X has no multisecant c-space. In this paper we extend this result by classifying varieties with index(X) ≥ c - s or with no multisecant (c - s)-space for s = 1 and 2.

Original language	English
Pages (from-to)	525-530
Number of pages	6
Journal	Archiv der Mathematik
Volume	96
Issue number	6
DOIs	https://doi.org/10.1007/s00013-011-0270-1
Publication status	Published - 2011 Jun

Keywords

Green-Lazarsfeld index
Multisecant space
Variety of low degree

ASJC Scopus subject areas

Mathematics(all)

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title = "On multisecants and the Green-Lazarsfeld index of projective varieties",

abstract = "It is well known that a nondegenerate projective subvariety X ⊂ ℙr of degree d and codimension c > 1 has minimal degree (i.e., d = c + 1) if and only if index(X) ≥ c if and only if X has no multisecant c-space. In this paper we extend this result by classifying varieties with index(X) ≥ c - s or with no multisecant (c - s)-space for s = 1 and 2.",

keywords = "Green-Lazarsfeld index, Multisecant space, Variety of low degree",

author = "Wanseok Lee and Euisung Park and Youngho Woo",

note = "Funding Information: The first and third named authors were supported by the National Researcher program 2010-0020413 of NRF and MEST. The second named author was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (No. 20090073305).",

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AU - Park, Euisung

AU - Woo, Youngho

N1 - Funding Information: The first and third named authors were supported by the National Researcher program 2010-0020413 of NRF and MEST. The second named author was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (No. 20090073305).

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N2 - It is well known that a nondegenerate projective subvariety X ⊂ ℙr of degree d and codimension c > 1 has minimal degree (i.e., d = c + 1) if and only if index(X) ≥ c if and only if X has no multisecant c-space. In this paper we extend this result by classifying varieties with index(X) ≥ c - s or with no multisecant (c - s)-space for s = 1 and 2.

AB - It is well known that a nondegenerate projective subvariety X ⊂ ℙr of degree d and codimension c > 1 has minimal degree (i.e., d = c + 1) if and only if index(X) ≥ c if and only if X has no multisecant c-space. In this paper we extend this result by classifying varieties with index(X) ≥ c - s or with no multisecant (c - s)-space for s = 1 and 2.

KW - Green-Lazarsfeld index

KW - Multisecant space

KW - Variety of low degree

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