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Article #10Re: Fano varieties
From: Valery A. Alexeev
Date: Tue, 03 Nov 1992 19:12
Date: Tue, 03 Nov 1992 19:12
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Answer: the only connection: Fano is the author of both gadgets. They couldn't mean the same thing: For the first definitition take any variety X and 0-planes, contained in it, you get X again. If you don't like 0-dimensional planes, then take a Veronese embedding of X and then a cone over it, or a scroll. F_1(Y) will be evidently isomorphic to X. You can take a cone again or P^2-fibration to get 2-planes and so on. I guess Fano studied lines in a 3-dimensional cubic. They are parametrized by a so called Fano surface (of this cubic). In the second definition on the other hand we have very specific varieties. V.
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Newsgroups: sci.math.research Path: arc1-ca.pugleaf.net!sparky!uunet!think.com!sdd.hp.com!ux1.cso.uiuc.edu!news.cso.uiuc.edu!usenet From: alexeev@math.utah.edu (Valery A. Alexeev) Subject: Re: Fano varieties References: <1992Nov3.75245.17867@ms.uky.edu> Message-ID: <ALEXEEV.92Nov3141223@solitude.math.utah.edu> Sender: Daniel Grayson <dan@math.uiuc.edu> X-Submissions-To: sci-math-research@uiuc.edu Organization: Department of Mathematics, University of Utah X-Administrivia-To: sci-math-research-request@uiuc.edu Approved: Daniel Grayson <dan@math.uiuc.edu> In-Reply-To: cyeomans@ms.uky.edu's message of Tue, 3 Nov 1992 12:52:45 GMT Date: Tue, 3 Nov 1992 19:12:23 GMT Lines: 16