On the geometry of generalized quadrics

Mohan Kumar, N. ; Rao, A. P. ; Ravindra, G. V. (2007) On the geometry of generalized quadrics Journal of Pure and Applied Algebra, 208 (3). pp. 1051-1054. ISSN 0022-4049

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Official URL: http://dx.doi.org/10.1016/j.jpaa.2006.05.014

Related URL: http://dx.doi.org/10.1016/j.jpaa.2006.05.014


Let {f0,…,fn;g0,…,gn} be a sequence of homogeneous polynomials in 2n+2 variables with no common zeros in P2n+1and suppose that the degrees of the polynomials are such that Q=Σni=0figi 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.

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