Timeline for Irreducibility of intersections of quadric hypersurfaces
Current License: CC BY-SA 3.0
12 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Dec 9, 2011 at 15:36 | comment | added | Fei YE | Hi Jack, You can assume that $i$, $j$, $k$ vary in the natural number set and intersection is taken in the complex affine space of those variables. The equations are determinants of $2\times 2$ matrices [\begin{vmatrix} x_2-x_1& y_{2i}-y_{1j}\\ x_3-x_1& y_{3k}-y_{1j} \end{vamtraix}.] | |
| Dec 9, 2011 at 15:30 | history | edited | Fei YE | CC BY-SA 3.0 |
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| Dec 9, 2011 at 8:01 | answer | added | Martin Bright | timeline score: 2 | |
| Dec 8, 2011 at 22:30 | answer | added | cdm80 | timeline score: 2 | |
| Dec 8, 2011 at 18:13 | comment | added | Jack Huizenga | What space does the intersection take place in, and how do $i,j,k$ vary? Also, where does this come from? Typically studying the geometric properties of a variety by studying its defining equations is a difficult thing to do. If these came up more naturally as determinantal varieties or something, that could perhaps be useful. | |
| Dec 8, 2011 at 14:41 | history | edited | Fei YE | CC BY-SA 3.0 |
added 147 characters in body
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| Dec 8, 2011 at 14:38 | comment | added | Fei YE | Hey, thanks for the comments. I have edited my question to reflect the concern. Thanks again! | |
| Dec 8, 2011 at 14:31 | history | edited | Fei YE | CC BY-SA 3.0 |
added 195 characters in body
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| Dec 6, 2011 at 20:57 | comment | added | meh | For example, take the two quadrics; $f = x^2 + y^2 + z^2 +w^2$ and $g = x^2 + y^2 - z^2 -w^2$ . Then the ideal $I =(f,g) = (x^2 + y^2,z^2 +w^2)$ which is 4 lines. Hard to find two nicer quadrics. | |
| Nov 30, 2011 at 15:01 | comment | added | Jack Huizenga | What exactly are you looking for? The obvious (although sarcastic-sounding) answer is "Sometimes," and it's hard to improve on that answer without further information. | |
| Nov 30, 2011 at 9:34 | history | asked | Fei YE | CC BY-SA 3.0 |