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Exceptional sequences of invertible sheaves on rational surfaces

  • Lutz Hille (a1) and Markus Perling (a2)
Abstract
Abstract

In this article we consider exceptional sequences of invertible sheaves on smooth complete rational surfaces. We show that to every such sequence one can associate a smooth complete toric surface in a canonical way. We use this structural result to prove various theorems on exceptional and strongly exceptional sequences of invertible sheaves on rational surfaces. We construct full strongly exceptional sequences for a large class of rational surfaces. For the case of toric surfaces we give a complete classification of full strongly exceptional sequences of invertible sheaves.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[Ful93] W. Fulton , Introduction to toric varieties (Princeton University Press, Princeton, NJ, 1993).

[GKZ94] I. M. Gelfand , M. M. Kapranov and A. V. Zelevinsky , Discriminants, resultants and multidimensional determinants, Mathematics: Theory & Applications (Birkhäuser, Boston, MA, 1994).

[Hap88] D. Happel , Triangulated categories in the representation theory of finite-dimensional algebras, London Mathematical Society Lecture Note Series, vol. 119 (Cambridge University Press, Cambridge, 1988).

[Har77] R. Hartshorne , Algebraic geometry, Graduate Texts in Mathematics, vol. 52 (Springer, Berlin, 1977).

[Hv07] L. Hille and M. van den Bergh , Fourier–Mukai transforms, in Handbook of tilting theory, London Mathematical Society Lecture Note Series, vol. 332 (Cambridge University Press, Cambridge, 2007), 147177.

[Huy06] D. Huybrechts , Fourier–Mukai transforms in algebraic geometry, Oxford Mathematical Monographs (Oxford University Press, Oxford, 2006).

[Rud90] A. N. Rudakov , Helices and vector bundles: seminaire Rudakov, London Mathematical Society Lecture Note Series, vol. 148 (Cambridge University Press, Cambridge, 1990).

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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
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