Comptes Rendus
no. 1-2
Algebraic Geometry
Family of counterexamples to King's conjecture
Presented by: the Editorial Board
Mateusz Michałek1, 2
1 Mathematical Institute of the Polish Academy of Sciences, Św. Tomasza 30, 31-027 Kraków, Poland
2 Institut Fourier, universite Joseph-Fourier, 100, rue des Maths, BP 74, 38402 St Martin d'Hères, France
Comptes Rendus. Mathématique, Volume 349 (2011) no. 1-2, pp. 67-69

In this short Note we present an infinite family of arbitrary high dimensional counterexamples to the King's conjecture.

Dans cette Note nous présentons une famille infinie de contre-exemples à la conjecture de A. King, de dimension arbitrairement grande.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2010.11.027

Mateusz Michałek 1, 2

1 Mathematical Institute of the Polish Academy of Sciences, Św. Tomasza 30, 31-027 Kraków, Poland
2 Institut Fourier, universite Joseph-Fourier, 100, rue des Maths, BP 74, 38402 St Martin d'Hères, France 
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Mateusz Michałek. Family of counterexamples to King's conjecture. Comptes Rendus. Mathématique, Volume 349 (2011) no. 1-2, pp. 67-69. doi: 10.1016/j.crma.2010.11.027

[1] V.V. Batyrev On the classification of smooth projective toric varieties, Tôhoku Math. J., Volume 43 (1991), pp. 569-585

[2] L. Costa, R.M. Miró-Roig, Derived category of toric varieties with small Picard number, preprint.

[3] L. Costa; R.M. Miró-Roig Tilting sheaves on toric varieties, Math. Z., Volume 248 (2004) no. 4, pp. 849-865

[4] L. Hille; M. Perling A counterexample to King's conjecture, Compos. Math., Volume 142 (2006), pp. 1507-1521

[5] L. Hille, M. Perling, Exceptional sequences of invertible sheaves on rational surfaces, Compos. Math., , in press. | arXiv

[6] A. King, Titling bundles on some rational surfaces, preprint at http://www.maths.bath.ac.uk/~masadk/papers/.

[7] M. Lason, M. Michalek, On the derived categories of toric varieties with Picard number three, preprint.

Cited by Sources:

☆ The author was supported by a grant of Polish MNiSW (N N201 413539).

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