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Article #9Fano varieties
From: Charles Yeomans
Date: Tue, 03 Nov 1992 12:52
Date: Tue, 03 Nov 1992 12:52
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I have seen a couple of ways to define a gadget called a Fano variety. First, let V be a variety in projective space. Then one may define F_k(V) to be the space of k-dimensional planes contained in V. Clearly, this variety is a subvariety of a Grassmann variety. Second, I have seen a Fano variety defined to be a variety for which -1 times the canonical class is ample. My question is, should these two definitions define the same object? If so, any hints as to how one might see that? Charles Yeomans cyeomans@ms.uky.edu yeomans@austin.onu.edu
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Newsgroups: sci.math.research Path: arc1-ca.pugleaf.net!sparky!uunet!spool.mu.edu!uwm.edu!ux1.cso.uiuc.edu!news.cso.uiuc.edu!usenet From: cyeomans@ms.uky.edu (Charles Yeomans) Subject: Fano varieties Message-ID: <1992Nov3.75245.17867@ms.uky.edu> Sender: Daniel Grayson <dan@math.uiuc.edu> X-Submissions-To: sci-math-research@uiuc.edu Organization: University Of Kentucky, Dept. of Math Sciences X-Administrivia-To: sci-math-research-request@uiuc.edu Approved: Daniel Grayson <dan@math.uiuc.edu> Date: Tue, 3 Nov 1992 12:52:45 GMT Lines: 16