Skip to main content

sl2-Structures on \({\mathcal{F}}^{{\prime}}\)

  • 1075 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 2072)

Abstract

The morphism d + (resp. d ) considered in §5, (5.26) [resp. (5.35)], attaches intrinsically the nilpotent endomorphism d +(v) (resp. d (v)) to every tangent vector v in T π.

Keywords

  • Tangent Vector
  • Homogeneous Space
  • Hodge Structure
  • Nilpotent Element
  • Sheaf Version

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    For this and other standard facts about such triples we refer to [Kos].

  2. 2.

    See Definition 4.22; from the results in §4.2, Theorem 4.26, it follows that this assumption is inessential.

  3. 3.

    Recall, by (5.2), the fibre \(\tilde{{\mathcal{F}}}^{{\prime}}([Z])\) does not depend on [α].

  4. 4.

    This terminology is explained in the footnote on page 7.

  5. 5.

    Since the component \(\Gamma \) is assumed to be simple, the sheaf \(\boldsymbol{\mathcal{G}}_{\Gamma }\), by Corollary 4.23, is actually a sheaf of simple Lie algebras. But this will not matter in the constructions below.

  6. 6.

    From Corollary 4.23 we know that \(\boldsymbol{\mathcal{G}}_{\Gamma } = \mathbf{sl}(\tilde{{\mathcal{F}}}^{{\prime}})\).

References

  1. B. Kostant, The principal three-dimensional subgroups and the Betti numbers of a complex simple Lie group. Am. J. Math. 81, 973–1032 (1959)

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. I. Reider, Nonabelian Jacobian of smooth projective surfaces. J. Differ. Geom. 74, 425–505 (2006)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Reider, I. (2013). sl2-Structures on \({\mathcal{F}}^{{\prime}}\) . 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_6

Download citation