Abstract
The construction of sl 2-structure in the previous section could have been done for any locally free sheaf of graded modules equipped with a compatible graded action of the sheaf of graded Lie algebras \(\boldsymbol{\mathcal{G}}_{\Gamma }\), where the grading on \(\boldsymbol{\mathcal{G}}_{\Gamma }\) is as described in §4.3, (4.72).
Keywords
- Basic Property
- Natural Projection
- Adjoint Action
- Multilinear Algebra
- Weight Filtration
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- 1.
Recall: (1) by Remark 5.3 the values of \(d_{\tau }^{+}\) are the same as the values of the morphism D + in the triangular decomposition in (2.63), and (2) the image of \({D}^{+}(\mathbf{\tilde{H}})\), by [R1], Lemma 7.6, is a subsheaf of abelian Lie subalgebra of \(\mathcal{G}_{\Gamma }\).
References
I. Reider, Nonabelian Jacobian of smooth projective surfaces. J. Differ. Geom. 74, 425–505 (2006)
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Reider, I. (2013). sl2-Structures on \({\mathcal{G}}_{\Gamma }\) . In: Nonabelian Jacobian of Projective Surfaces. Lecture Notes in Mathematics, vol 2072. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35662-9_7
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DOI: https://doi.org/10.1007/978-3-642-35662-9_7
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