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- W3119489039 abstract "Abstract To a quiver Q and choices of nonzero scalars $$q_i$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>q</mml:mi> <mml:mi>i</mml:mi> </mml:msub> </mml:math> , non-negative integers $$alpha _i$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>i</mml:mi> </mml:msub> </mml:math> , and integers $$theta _i$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>θ</mml:mi> <mml:mi>i</mml:mi> </mml:msub> </mml:math> labeling each vertex i , Crawley-Boevey–Shaw associate a multiplicative quiver variety $${mathcal {M}}_theta ^q(alpha )$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mi>θ</mml:mi> <mml:mi>q</mml:mi> </mml:msubsup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>α</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , a trigonometric analogue of the Nakajima quiver variety associated to Q , $$alpha $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>α</mml:mi> </mml:math> , and $$theta $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>θ</mml:mi> </mml:math> . We prove that the pure cohomology, in the Hodge-theoretic sense, of the stable locus $${mathcal {M}}_theta ^q(alpha )^{{text {s}}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mi>θ</mml:mi> <mml:mi>q</mml:mi> </mml:msubsup> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>α</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mtext>s</mml:mtext> </mml:msup> </mml:mrow> </mml:math> is generated as a $${mathbb {Q}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>Q</mml:mi> </mml:math> -algebra by the tautological characteristic classes. In particular, the pure cohomology of genus g twisted character varieties of $$GL_n$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>G</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:mrow> </mml:math> is generated by tautological classes." @default.
- W3119489039 created "2021-01-18" @default.
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- W3119489039 date "2021-01-13" @default.
- W3119489039 modified "2023-10-16" @default.
- W3119489039 title "The pure cohomology of multiplicative quiver varieties" @default.
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- W3119489039 doi "https://doi.org/10.1007/s00029-020-00606-1" @default.
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