Secant cumulants and toric geometry

M. Michalek, L. Oeding, P.W. Zwiernik

Research output: Book/ReportReportAcademic

Abstract

We study the secant line variety of the Segre product of projective spaces using special cumulant coordinates adapted for secant varieties. We show that the secant variety is covered by open normal toric varieties. We prove that in cumulant coordinates its ideal is generated by binomial quadrics. We present new results on the local structure of the secant variety. In particular, we show that it has rational singularities and we give a description of the singular locus. Generalizing results of Sturmfels and Zwiernik, we also show analogous results for the tangential variety.
Original languageEnglish
Publishers.n.
Publication statusPublished - 2012

Publication series

NamearXiv.org
Volume1212.1516 [math.AG]

Fingerprint

Secant Varieties
Cumulants
Chord or secant line
Rational Singularities
Toric Varieties
Local Structure
Quadric
Projective Space
Locus

Cite this

Michalek, M., Oeding, L., & Zwiernik, P. W. (2012). Secant cumulants and toric geometry. (arXiv.org; Vol. 1212.1516 [math.AG]). s.n.
Michalek, M. ; Oeding, L. ; Zwiernik, P.W. / Secant cumulants and toric geometry. s.n., 2012. (arXiv.org).
@book{810a8e3209ff4961b1bd329ac5ab9208,
title = "Secant cumulants and toric geometry",
abstract = "We study the secant line variety of the Segre product of projective spaces using special cumulant coordinates adapted for secant varieties. We show that the secant variety is covered by open normal toric varieties. We prove that in cumulant coordinates its ideal is generated by binomial quadrics. We present new results on the local structure of the secant variety. In particular, we show that it has rational singularities and we give a description of the singular locus. Generalizing results of Sturmfels and Zwiernik, we also show analogous results for the tangential variety.",
author = "M. Michalek and L. Oeding and P.W. Zwiernik",
year = "2012",
language = "English",
series = "arXiv.org",
publisher = "s.n.",

}

Michalek, M, Oeding, L & Zwiernik, PW 2012, Secant cumulants and toric geometry. arXiv.org, vol. 1212.1516 [math.AG], s.n.

Secant cumulants and toric geometry. / Michalek, M.; Oeding, L.; Zwiernik, P.W.

s.n., 2012. (arXiv.org; Vol. 1212.1516 [math.AG]).

Research output: Book/ReportReportAcademic

TY - BOOK

T1 - Secant cumulants and toric geometry

AU - Michalek, M.

AU - Oeding, L.

AU - Zwiernik, P.W.

PY - 2012

Y1 - 2012

N2 - We study the secant line variety of the Segre product of projective spaces using special cumulant coordinates adapted for secant varieties. We show that the secant variety is covered by open normal toric varieties. We prove that in cumulant coordinates its ideal is generated by binomial quadrics. We present new results on the local structure of the secant variety. In particular, we show that it has rational singularities and we give a description of the singular locus. Generalizing results of Sturmfels and Zwiernik, we also show analogous results for the tangential variety.

AB - We study the secant line variety of the Segre product of projective spaces using special cumulant coordinates adapted for secant varieties. We show that the secant variety is covered by open normal toric varieties. We prove that in cumulant coordinates its ideal is generated by binomial quadrics. We present new results on the local structure of the secant variety. In particular, we show that it has rational singularities and we give a description of the singular locus. Generalizing results of Sturmfels and Zwiernik, we also show analogous results for the tangential variety.

M3 - Report

T3 - arXiv.org

BT - Secant cumulants and toric geometry

PB - s.n.

ER -

Michalek M, Oeding L, Zwiernik PW. Secant cumulants and toric geometry. s.n., 2012. (arXiv.org).