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On quadrics of higher codimension

Name: On quadrics of higher codimension
Creator: N. F. Palinchak
Keywords: Low codimension problems in algebraic geometry, automorphisms, 0103 physical sciences, Automorphisms of surfaces and higher-dimensional varieties, 0101 mathematics, quadrics, 01 natural sciences, Birational automorphisms, Cremona group and generalizations

descriptionPublicationkeyboard_double_arrow_right Article 01 May 1994Publisher:Springer Science and Business Media LLCJournal:Mathematical Notes, volume 55, pages 512-516 (issn: 0001-4346, eissn: 1573-8876,

Authors: N. F. Palinchak;

doi: 10.1007/bf02110379

On quadrics of higher codimension

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Abstract

\textit{V. V. Ezov} and \textit{G. Schmalz}: [in the work ``A matrix Poincaré formula for holomorphic automorphisms of real associative quadrics'' (preprint)] selected quadrics, called RAQ quadrics, from all \((n,n)\)-quadrics. One has obtained a formula for the automorphisms of RAQ quadrics, preserving the origin. In connection with this there arose the following question: Is it true that among the irreducible quadrics only the RAQ quadrics have nonlinear automorphisms? The answer is negative, in \(\mathbb{C}^6\) there exists an irreducible quadric with nonlinear automorphisms, which is not a RAQ quadric.

Related Organizations

Lomonosov Moscow State University
Russian Federation

Keywords

Low codimension problems in algebraic geometry, automorphisms, Automorphisms of surfaces and higher-dimensional varieties, quadrics, Birational automorphisms, Cremona group and generalizations

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