On the geometry of generalized quadrics

N. Mohan Kumar; Prabhakar Rao; G. V. Ravindra

doi:10.1016/j.jpaa.2006.05.014

On the geometry of generalized quadrics

N. Mohan Kumar, Prabhakar Rao, G. V. Ravindra

University of Missouri-St. Louis

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

Abstract

Let {f0,…,fn;g0,…,gn} be a sequence of homogeneous polynomials in 2n+2 variables with no common zeros in P2n+1 and suppose that the degrees of the polynomials are such that Q=∑i=0nfigi is a homogeneous polynomial. We shall refer to the hypersurface X defined by Q as a generalized quadric . In this note, we prove that generalized quadrics in PC2n+1 for n≥1 are reduced.

Original language	American English
Journal	Journal of Pure and Applied Algebra
Volume	208
DOIs	https://doi.org/10.1016/j.jpaa.2006.05.014
State	Published - Mar 2007

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Computer Sciences

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title = "On the geometry of generalized quadrics",

abstract = " Let \{f0,…,fn;g0,…,gn\} be a sequence of homogeneous polynomials in 2n+2 variables with no common zeros in P2n+1 and suppose that the degrees of the polynomials are such that Q=∑i=0nfigi is a homogeneous polynomial. We shall refer to the hypersurface X defined by Q as a generalized quadric . In this note, we prove that generalized quadrics in PC2n+1 for n≥1 are reduced. ",

author = "Kumar, \{N. Mohan\} and Prabhakar Rao and Ravindra, \{G. V.\}",

year = "2007",

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volume = "208",

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AU - Rao, Prabhakar

AU - Ravindra, G. V.

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N2 - Let {f0,…,fn;g0,…,gn} be a sequence of homogeneous polynomials in 2n+2 variables with no common zeros in P2n+1 and suppose that the degrees of the polynomials are such that Q=∑i=0nfigi is a homogeneous polynomial. We shall refer to the hypersurface X defined by Q as a generalized quadric . In this note, we prove that generalized quadrics in PC2n+1 for n≥1 are reduced.

AB - Let {f0,…,fn;g0,…,gn} be a sequence of homogeneous polynomials in 2n+2 variables with no common zeros in P2n+1 and suppose that the degrees of the polynomials are such that Q=∑i=0nfigi is a homogeneous polynomial. We shall refer to the hypersurface X defined by Q as a generalized quadric . In this note, we prove that generalized quadrics in PC2n+1 for n≥1 are reduced.

UR - https://doi.org/10.1016/j.jpaa.2006.05.014

U2 - 10.1016/j.jpaa.2006.05.014

DO - 10.1016/j.jpaa.2006.05.014

M3 - Article

VL - 208

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

ER -

On the geometry of generalized quadrics

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