Vol. 8, No. 4, 2015

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Some projective distance inequalities for simplices in complex projective space

Mark Fincher, Heather Olney and William Cherry

Vol. 8 (2015), No. 4, 707–719
Abstract

We prove inequalities relating the absolute value of the determinant of n + 1 linearly independent unit vectors in n+1 and the projective distances from the vertices to the hyperplanes containing the opposite faces of the simplices in complex projective n-space whose vertices or faces are determined by the given vectors.

Keywords
projective height, projective simplex, determinant
Mathematical Subject Classification 2010
Primary: 51N15
Secondary: 32Q45
Milestones
Received: 22 July 2014
Accepted: 19 August 2014
Published: 23 June 2015

Communicated by Michael Dorff
Authors
Mark Fincher
Department of Mathematics
University of North Texas
1155 Union Circle #311430
Denton, TX 76203
United States
Heather Olney
Department of Mathematics
University of North Texas
1155 Union Circle #311430
Denton, TX 76203
United States
William Cherry
Department of Mathematics
University of North Texas
1155 Union Circle #311430
Denton, TX 76203
United States