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In Fulton's 'Introduction to Toric Varieties' in section 2.5, there is an exercise (top of p44 in my book) which reads 'If $d \geq 4$ then there must be 2 opposite vectors in the sequence'.

Is this a typo? For example, is there a problem with the seqence $(1,0),(1,1),(0,1),(-1,1)$? If it is a typo, does replacing 4 with 5 make it correct?


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You have to specify more if you want help with this - not everyone have a copy of Fulton's book lying around. Also, perhaps this question might be better suited for math.stackexchange.com. –  J.C. Ottem Nov 19 '10 at 16:19
There is indeed a problem with your sequence; the (three) convex cones don't cover the whole of R². (Fulton is dealing with complete surfaces here, see the previous section). Actually in p.42 he demands that v_d=v_0, so you should add (1,0) at the end of the sequence to be consistent with his notation; you'd get a fourth cone, but unfortunately that cone contains the other vectors so... –  quim Nov 19 '10 at 16:38
Thanks for your reply. –  Robert Garbary Nov 19 '10 at 18:02
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