A note on generic projections |
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Authors: | Email author" target="_blank">Hubert?FlennerEmail author Mirella?Manaresi |
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Institution: | (1) Hubert Flenner, Fakultät für Mathematik der Ruhr-Universität, Geb. NA 2/72, 44780 Bochum, Germany;(2) Mirella Manaresi, Dipartimento di Matematica, Università, P.za di Porta S. Donato 5, 40126 Bologna, Italy |
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Abstract: | Let XN=2nK be a subvariety of dimension n and PN a generic point. If the tangent variety TanX is equal to N then for generic points x, y of X the projective tangent spaces txX and tyX meet in one point P=P(x,y). The main result of this paper is that the rational map (x,y)P(x,y) is dominant. In other words, a generic point P is uniquely determined by the ramification locus R(P) of the linear projection P:XN–1.This paper was supported by the DFG Schwerpunkt Global methods in complex analysis, MUR and the Research Group GNSAGA of INDAM. This investigation was also supported by the University of Bologna, funds for selected research topics |
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