Comments for Rigorous Trivialities http://rigtriv.wordpress.com Thu, 16 May 2013 21:18:02 +0000 hourly 1 http://wordpress.com/ Comment on Affine Varieties by Anonymous http://rigtriv.wordpress.com/2007/12/18/affine-varieties/#comment-4301 Thu, 16 May 2013 21:18:02 +0000 http://rigtriv.wordpress.com/2007/12/18/affine-varieties/#comment-4301 Aah! Thank you for spelling that out.

]]> Comment on The Twenty-Seven Lines on the Cubic Surface by Charles Siegel http://rigtriv.wordpress.com/2008/06/18/the-twenty-seven-lines-on-the-cubic-surface/#comment-4264 Mon, 06 May 2013 00:54:35 +0000 http://rigtriv.wordpress.com/?p=140#comment-4264 The reference where I learned it was, if I recall correctly, Hulek’s “Elementary Algebraic Geometry.”

]]> Comment on The Twenty-Seven Lines on the Cubic Surface by Seth Neel http://rigtriv.wordpress.com/2008/06/18/the-twenty-seven-lines-on-the-cubic-surface/#comment-4263 Sun, 05 May 2013 23:57:06 +0000 http://rigtriv.wordpress.com/?p=140#comment-4263 where can i find a proof using the resultant?

]]> Comment on Morphisms of Sheaves by Charles Siegel http://rigtriv.wordpress.com/2008/01/30/morphisms-of-sheaves/#comment-4251 Sat, 27 Apr 2013 04:50:10 +0000 http://rigtriv.wordpress.com/?p=81#comment-4251 Of course. Thanks, I’ll go fix that.

]]> Comment on Morphisms of Sheaves by mlbaker http://rigtriv.wordpress.com/2008/01/30/morphisms-of-sheaves/#comment-4249 Sat, 27 Apr 2013 01:12:02 +0000 http://rigtriv.wordpress.com/?p=81#comment-4249 A morphism of sheaves is an abelian group homomorphism \phi(U) : \mathscr{F}(U) \to \mathscr{G}(U) for each open set U, not \phi(U) : \mathscr{F} \to \mathscr{G}…

]]> Comment on Blowing things up by Tittu http://rigtriv.wordpress.com/2008/07/09/blowing-things-up/#comment-4241 Tue, 23 Apr 2013 05:49:17 +0000 http://rigtriv.wordpress.com/?p=154#comment-4241 Thanks!

]]> Comment on Affine Varieties by Charles Siegel http://rigtriv.wordpress.com/2007/12/18/affine-varieties/#comment-4236 Mon, 22 Apr 2013 00:10:39 +0000 http://rigtriv.wordpress.com/2007/12/18/affine-varieties/#comment-4236 I perhaps should, but thanks to the Hilbert Basis Theorem, which says that every ideal in \mathbb{C}[x_1,\ldots,x_n] is finitely generated, we have that any infinite set of polynomials generates an ideal of all things that vanish on their common zeros (up to taking radicals), and then that ideal is actually finitely generated, so only finitely many polynomials suffice.

]]> Comment on Affine Varieties by luke sciarappa http://rigtriv.wordpress.com/2007/12/18/affine-varieties/#comment-4235 Sun, 21 Apr 2013 22:23:01 +0000 http://rigtriv.wordpress.com/2007/12/18/affine-varieties/#comment-4235 Shouldn’t an algebraic set be the common zeroes of an arbitrary (not necessarily finite) collection of sets? Otherwise I don’t see how they’re closed under arbitrary intersection.

]]> Comment on Blowing things up by Charles Siegel http://rigtriv.wordpress.com/2008/07/09/blowing-things-up/#comment-4221 Mon, 15 Apr 2013 09:58:06 +0000 http://rigtriv.wordpress.com/?p=154#comment-4221 Well, blowing up is an isomorphism away from locus blown up, so first remember that projective space doesn’t HAVE an origin. Then, you take your projective space, choose coordinates to make the point you’re blowing up the 0 of some affine chart, and blow that up, but then you can glue the whole thing back together with (essentially) the same gluing map, because away from p and \pi^{-1}(p), the blowup map is an isomorphism.

]]> Comment on Blowing things up by Tittu http://rigtriv.wordpress.com/2008/07/09/blowing-things-up/#comment-4220 Mon, 15 Apr 2013 05:26:08 +0000 http://rigtriv.wordpress.com/?p=154#comment-4220 From the post I have clearly understood the blowing up affine n-space at the origin. Now , how to blow up projective n-space at the origin?

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