On maximum, typical and generic ranks

Grigoriy Blekherman; Zach Teitler

doi:10.1007/s00208-014-1150-3

On maximum, typical and generic ranks

Grigoriy Blekherman
, Zach Teitler

Mathematics Department

Georgia Tech Research Corporation

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

68 Scopus citations

Abstract

We show that for several notions of rank including tensor rank, Waring rank, and generalized rank with respect to a projective variety, the maximum value of rank is at most twice the generic rank. We show that over the real numbers, the maximum value of the real rank is at most twice the smallest typical rank, which is equal to the (complex) generic rank.

Original language	English
Pages (from-to)	1021-1031
Number of pages	11
Journal	Mathematische Annalen
Volume	362
Issue number	3-4
DOIs	https://doi.org/10.1007/s00208-014-1150-3
State	Published - 3 Dec 2015

Keywords

14N15
15A21
15A69

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10.1007/s00208-014-1150-3

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title = "On maximum, typical and generic ranks",

abstract = "We show that for several notions of rank including tensor rank, Waring rank, and generalized rank with respect to a projective variety, the maximum value of rank is at most twice the generic rank. We show that over the real numbers, the maximum value of the real rank is at most twice the smallest typical rank, which is equal to the (complex) generic rank.",

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AU - Teitler, Zach

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N2 - We show that for several notions of rank including tensor rank, Waring rank, and generalized rank with respect to a projective variety, the maximum value of rank is at most twice the generic rank. We show that over the real numbers, the maximum value of the real rank is at most twice the smallest typical rank, which is equal to the (complex) generic rank.

AB - We show that for several notions of rank including tensor rank, Waring rank, and generalized rank with respect to a projective variety, the maximum value of rank is at most twice the generic rank. We show that over the real numbers, the maximum value of the real rank is at most twice the smallest typical rank, which is equal to the (complex) generic rank.

KW - 14N15

KW - 15A21

KW - 15A69

UR - https://www.scopus.com/pages/publications/84937526056

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DO - 10.1007/s00208-014-1150-3

M3 - Article

AN - SCOPUS:84937526056

SN - 0025-5831

VL - 362

SP - 1021

EP - 1031

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 3-4

ER -

On maximum, typical and generic ranks

Abstract

Keywords

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