Timeline for Canonical bundle of the Lagrangian Grassmannian
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Aug 17, 2016 at 11:47 | comment | added | L_K666 | I'm not able to log myself into my account L. Kern. Thus I had to build a new one but no reputations = not able to answer in comments. But thanks for those quick answers, I think @Jason Starrs answer might help. | |
| Aug 15, 2016 at 19:22 | answer | added | Friedrich Knop | timeline score: 10 | |
| Aug 15, 2016 at 16:12 | comment | added | Jason Starr | The canonical bundle of the Grassmannian of $n$-dimensional subspaces of a $2n$-dimensional vector space equals $\mathcal{O}(-2n)$. Thus you need to compute the normal bundle of the Lagrangian Grassmannian as a subvariety of the classical Grassmannian. Denoting by $\mathcal{O}^{\oplus 2n}\to S^\vee$ the universal quotient that is locally free of rank $n$, then the Lagrangian Grassmannian is the zero locus of a section of $\bigwedge^2 S^\vee$. This has first Chern class $(n-1)c_1(\mathcal{O}(1))$. Thus the canonical bundle is $\mathcal{O}((-2n) + (n-1))$. | |
| Aug 15, 2016 at 13:20 | review | First posts | |||
| Aug 15, 2016 at 13:36 | |||||
| Aug 15, 2016 at 13:19 | history | asked | L. Kern | CC BY-SA 3.0 |