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GIT-Equivalence and Diagonal Actions
P. Yu. Kotenkova M. V. Lomonosov Moscow State University
Abstract:
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, diagonal action, GIT-equivalence, Picard group, fan of cones, GIT-fan
DOI:
https://doi.org/10.4213/mzm8776
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English version:
Mathematical Notes, 2011, 90:2, 250–259
Bibliographic databases:
UDC:
512.745.2 Received: 17.02.2010 Revised: 18.10.2010
Citation:
P. Yu. Kotenkova, “GIT-Equivalence and Diagonal Actions”, Mat. Zametki, 90:2 (2011), 269–279; Math. Notes, 90:2 (2011), 250–259
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/mz8776https://doi.org/10.4213/mzm8776 http://mi.mathnet.ru/eng/mz/v90/i2/p269
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