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Results tagged with picard-group
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user 4149
5
votes
Accepted
Picard group of symplectic group modulo orthogonal group
Answer: ${\rm Pic\,} X={\Bbb Z}/2{\Bbb Z}$; see Corollary 4 below.
Theorem 1. Let $G$ be a simply connected semisimple group over a field $k$ of characteristic 0.
Let $H\subset G$ be an alge …
- 14.2k
4
votes
Accepted
Picard group of $\mathrm{GL}(n)$-orbits
$\DeclareMathOperator\Pic{Pic}\DeclareMathOperator\GL{GL}\DeclareMathOperator\GO{GO}$
Let $G$ be a connected linear algebraic group over an algebraically closed field $K$ of characteristic 0.
Let $ …
- 14.2k
2
votes
Picard group of $(SL(n)\times SL(m))$-orbits
Let $G={\rm SL}(n)\times {\rm SL}(n')$ and let $H\subset G$ denote the stabilizer of $J_k$ in $G$. We write ${\frak X}(G)$ for the character group of $G$. Then ${\frak X}(G)=0$. We have a canonical is …
- 14.2k