On 3 -linear varieties of codimension 2

Wanseok Lee; Euisung Park

doi:10.1142/S0219498820501066

On 3 -linear varieties of codimension 2

Wanseok Lee, Euisung Park

Department of Mathematics

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

Abstract

A projective variety in a projective space is said to be p-linear if it is p-regular and has no defining equation of degree < p. It is well known that 2-linear varieties are exactly varieties of minimal degree. In this paper, we study 3-linear varieties of codimension 2. We classify all smooth 3-linear varieties of codimension 2. There are six kinds of such varieties. Also, we provide some nonconic singular 3-linear varieties of codimension 2.

Original language	English
Article number	2050106
Journal	Journal of Algebra and its Applications
Volume	19
Issue number	6
DOIs	https://doi.org/10.1142/S0219498820501066
Publication status	Published - 2020 Jun 1

Keywords

Castelnuovo-Mumford regularity
linear resolution

ASJC Scopus subject areas

Algebra and Number Theory
Applied Mathematics

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10.1142/S0219498820501066

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title = "On 3 -linear varieties of codimension 2",

abstract = "A projective variety in a projective space is said to be p-linear if it is p-regular and has no defining equation of degree < p. It is well known that 2-linear varieties are exactly varieties of minimal degree. In this paper, we study 3-linear varieties of codimension 2. We classify all smooth 3-linear varieties of codimension 2. There are six kinds of such varieties. Also, we provide some nonconic singular 3-linear varieties of codimension 2.",

keywords = "Castelnuovo-Mumford regularity, linear resolution",

author = "Wanseok Lee and Euisung Park",

note = "Funding Information: The first author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2017R1D1A1B03031438). The second author was supported by the Korea Research Foundation Grant funded by the Korean Government (NRF-2018R1D1A1B07041336). The authors also thank the referee for a careful study of the manuscript and the suggested improvements. Publisher Copyright: {\textcopyright} 2020 World Scientific Publishing Company.",

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N2 - A projective variety in a projective space is said to be p-linear if it is p-regular and has no defining equation of degree < p. It is well known that 2-linear varieties are exactly varieties of minimal degree. In this paper, we study 3-linear varieties of codimension 2. We classify all smooth 3-linear varieties of codimension 2. There are six kinds of such varieties. Also, we provide some nonconic singular 3-linear varieties of codimension 2.

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JF - Journal of Algebra and Its Applications

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On 3 -linear varieties of codimension 2

Abstract

Keywords

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