Timeline for a net of quadrics and the corresponding intersection
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Mar 14, 2014 at 16:26 | comment | added | Roberto Pignatelli | "Span" means "the smallest linear space containing it". As an irreducible quadric can't be contained in a plane, its span must be that hyperplane, that has dimension 3. About your second question: let $H$ be this hyperplane, then $S'$ is contained in both $Q_1 \cap H$ and $Q_2 \cap H$. Since $S'$ is defined by a single quadratic relation in $H$, $Q_1$ and $Q_2$ are proportional modulo the equation of $H$, so a suitable combination of them vanishes along $H$. | |
| Mar 14, 2014 at 11:50 | comment | added | Sasga | Thank. In (2), I know that S′ is contained in a hyperplane. What's the meaning of "span"? Why a pencil of quadrics in the net contains this hyperplane? | |
| Mar 13, 2014 at 16:59 | history | answered | Roberto Pignatelli | CC BY-SA 3.0 |