A note on relative hemisystems of Hermitian generalised quadrangles

John Bamberg; Melissa Lee; Eric Swartz

doi:10.1007/s10623-015-0135-x

A note on relative hemisystems of Hermitian generalised quadrangles

John Bamberg, Melissa Lee, Eric Swartz

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

1 Citation (Scopus)

Abstract

In this paper we introduce a set of sufficient criteria for the construction of relative hemisystems of the Hermitian space H (3 , q²) , unifying all known infinite families. We use these conditions to provide new proofs of the existence of the known infinite families of relative hemisystems. Reproving these results has allowed us to find new relative hemisystems closely related to an infinite family of Cossidente’s, and develop techniques that are likely to be useful in finding relative hemisystems in future.

Original language	English
Pages (from-to)	131-144
Number of pages	14
Journal	Designs Codes and Cryptography
Volume	81
Issue number	1
DOIs	https://doi.org/10.1007/s10623-015-0135-x
Publication status	Published - 1 Oct 2016
Externally published	Yes

Keywords

Classical polar space
Hermitian variety
Relative hemisystem

Access to Document

10.1007/s10623-015-0135-xLicence: CC BY

Cite this

@article{b2dcf333b60c4326a22941cf92fe904c,

title = "A note on relative hemisystems of Hermitian generalised quadrangles",

abstract = "In this paper we introduce a set of sufficient criteria for the construction of relative hemisystems of the Hermitian space H (3 , q2) , unifying all known infinite families. We use these conditions to provide new proofs of the existence of the known infinite families of relative hemisystems. Reproving these results has allowed us to find new relative hemisystems closely related to an infinite family of Cossidente{\textquoteright}s, and develop techniques that are likely to be useful in finding relative hemisystems in future.",

keywords = "Classical polar space, Hermitian variety, Relative hemisystem",

author = "John Bamberg and Melissa Lee and Eric Swartz",

note = "Funding Information: The authors would like to express their thanks to Prof. Gordon Royle for his assistance in computation for this paper, and Dr. Angela Aguglia for her insight into intersections of hyperbolic quadrics with Hermitian spaces. The first author acknowledges the support of the Australian Research Council Future Fellowship FT120100036. The second author acknowledges the support of a Hackett Postgraduate Research Scholarship. The third author acknowledges the support of the Australian Research Council Discovery Grant DP120101336. Publisher Copyright: {\textcopyright} 2015, Springer Science+Business Media New York.",

year = "2016",

month = oct,

day = "1",

doi = "10.1007/s10623-015-0135-x",

language = "English",

volume = "81",

pages = "131--144",

journal = "Designs Codes and Cryptography",

issn = "0925-1022",

publisher = "Springer",

number = "1",

}

TY - JOUR

T1 - A note on relative hemisystems of Hermitian generalised quadrangles

AU - Bamberg, John

AU - Lee, Melissa

AU - Swartz, Eric

N1 - Funding Information: The authors would like to express their thanks to Prof. Gordon Royle for his assistance in computation for this paper, and Dr. Angela Aguglia for her insight into intersections of hyperbolic quadrics with Hermitian spaces. The first author acknowledges the support of the Australian Research Council Future Fellowship FT120100036. The second author acknowledges the support of a Hackett Postgraduate Research Scholarship. The third author acknowledges the support of the Australian Research Council Discovery Grant DP120101336. Publisher Copyright: © 2015, Springer Science+Business Media New York.

PY - 2016/10/1

Y1 - 2016/10/1

N2 - In this paper we introduce a set of sufficient criteria for the construction of relative hemisystems of the Hermitian space H (3 , q2) , unifying all known infinite families. We use these conditions to provide new proofs of the existence of the known infinite families of relative hemisystems. Reproving these results has allowed us to find new relative hemisystems closely related to an infinite family of Cossidente’s, and develop techniques that are likely to be useful in finding relative hemisystems in future.

AB - In this paper we introduce a set of sufficient criteria for the construction of relative hemisystems of the Hermitian space H (3 , q2) , unifying all known infinite families. We use these conditions to provide new proofs of the existence of the known infinite families of relative hemisystems. Reproving these results has allowed us to find new relative hemisystems closely related to an infinite family of Cossidente’s, and develop techniques that are likely to be useful in finding relative hemisystems in future.

KW - Classical polar space

KW - Hermitian variety

KW - Relative hemisystem

UR - https://www.scopus.com/pages/publications/84944535376

U2 - 10.1007/s10623-015-0135-x

DO - 10.1007/s10623-015-0135-x

M3 - Article

AN - SCOPUS:84944535376

SN - 0925-1022

VL - 81

SP - 131

EP - 144

JO - Designs Codes and Cryptography

JF - Designs Codes and Cryptography

IS - 1

ER -

A note on relative hemisystems of Hermitian generalised quadrangles

Abstract

Keywords

Access to Document

Other files and links

Cite this