Geodesic
GIT-Equivalence and Diagonal Actions
Matematičeskie zametki, Tome 90 (2011) no. 2, pp. 269-279

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In the paper, the GIT-equivalence classes of the linearized linear bundles for the diagonal actions of the linear algebraic groups $\operatorname{SL}(V)$ and $\operatorname{SO}(V)$ on the projective varieties $\mathbb{P}(V)^{m_1}\times\mathbb{P}(V^*)^{m_2}$ and $\mathbb{P}(V)^m$, respectively, are described explicitly.
Keywords: linearized linear bundle, projective variety, linear algebraic group, fan of cones
Mots-clés : diagonal action, GIT-equivalence, Picard group, GIT-fan. 
@article{MZM_2011_90_2_a8,
     author = {P. Yu. Kotenkova},
     title = {GIT-Equivalence and {Diagonal} {Actions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {269--279},
     publisher = {mathdoc},
     volume = {90},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_90_2_a8/}
}
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P. Yu. Kotenkova. GIT-Equivalence and Diagonal Actions. Matematičeskie zametki, Tome 90 (2011) no. 2, pp. 269-279. http://geodesic.mathdoc.fr/item/MZM_2011_90_2_a8/