Rank two jump loci for solvmanifolds and Lie algebras
キーワード:
representation variety,
characteristic variety,
resonance variety,
analytic germ,
solvmanifold,
Lie algebra
2018 年 70 巻 2 号 p. 695-709
詳細
2018 年 70 巻 2 号 p. 695-709
We consider representation varieties in 𝑆𝐿2 for lattices in solvable Lie groups, and representation varieties in 𝔰𝔩2 for finite-dimensional Lie algebras. Inside them, we examine depth 1 characteristic varieties for solvmanifolds, respectively resonance varieties for cochain Differential Graded Algebras of Lie algebras. We prove a general result that leads, in both cases, to the complete description of the analytic germs at the origin, for the corresponding embedded rank 2 jump loci.
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