A Zeuthen Segre formula for even dimensional submanifolds of real projective space

J.W. Bruce; P.J. Giblin

doi:10.1017/S0017089500005127

A Zeuthen Segre formula for even dimensional submanifolds of real projective space

J.W. Bruce, P.J. Giblin

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

Abstract

In this paper we generalise results of Craveiro de Carvalho ([3]) in two ways. First we prove the following fact. PROPOSITION 1. Given any smooth submanifold M of real projective space n, for L in an open dense subset of the space of codimension 2 subspaces of n we have (a) L meets M transversally and (b) the pencil of hyperplanes through L have at worst Morse (A1) contact with M.

Original language	English
Pages (from-to)	97-99
Journal	Glasgow Mathematical Journal
Volume	24
Issue number	1
DOIs	https://doi.org/10.1017/S0017089500005127
Publication status	Published - 1983

Access to Document

10.1017/S0017089500005127

Cite this

@article{845ab1bf4bc643b9ab8731f7af5cec37,

title = "A Zeuthen Segre formula for even dimensional submanifolds of real projective space",

abstract = "In this paper we generalise results of Craveiro de Carvalho ([3]) in two ways. First we prove the following fact. PROPOSITION 1. Given any smooth submanifold M of real projective space n, for L in an open dense subset of the space of codimension 2 subspaces of n we have (a) L meets M transversally and (b) the pencil of hyperplanes through L have at worst Morse (A1) contact with M.",

author = "J.W. Bruce and P.J. Giblin",

year = "1983",

doi = "10.1017/S0017089500005127",

language = "English",

volume = "24",

pages = "97--99",

journal = "Glasgow Mathematical Journal",

issn = "0017-0895",

publisher = "Cambridge University Press",

number = "1",

}

TY - JOUR

T1 - A Zeuthen Segre formula for even dimensional submanifolds of real projective space

AU - Bruce, J.W.

AU - Giblin, P.J.

PY - 1983

Y1 - 1983

N2 - In this paper we generalise results of Craveiro de Carvalho ([3]) in two ways. First we prove the following fact. PROPOSITION 1. Given any smooth submanifold M of real projective space n, for L in an open dense subset of the space of codimension 2 subspaces of n we have (a) L meets M transversally and (b) the pencil of hyperplanes through L have at worst Morse (A1) contact with M.

AB - In this paper we generalise results of Craveiro de Carvalho ([3]) in two ways. First we prove the following fact. PROPOSITION 1. Given any smooth submanifold M of real projective space n, for L in an open dense subset of the space of codimension 2 subspaces of n we have (a) L meets M transversally and (b) the pencil of hyperplanes through L have at worst Morse (A1) contact with M.

U2 - 10.1017/S0017089500005127

DO - 10.1017/S0017089500005127

M3 - Article (journal)

SN - 0017-0895

VL - 24

SP - 97

EP - 99

JO - Glasgow Mathematical Journal

JF - Glasgow Mathematical Journal

IS - 1

ER -

A Zeuthen Segre formula for even dimensional submanifolds of real projective space

Abstract

Access to Document

Fingerprint

Cite this