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Spherical functors on the Kummer surface

Part of: (Co)homology theory Surfaces and higher-dimensional varieties Abelian categories

Published online by Cambridge University Press:  11 January 2016

Andreas Krug  and
Ciaran Meachan
Andreas Krug
Affiliation:
Mathematisches Institut, Universität Bonn, Bonn, Germany, akrug@math.uni-bonn.de
Ciaran Meachan
Affiliation:
School of Mathematics University of Edinburgh, Edinburgh, Scotland, ciaran.meachan@ed.ac.uk
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Abstract

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We find two natural spherical functors associated to the Kummer surface and analyze how their induced twists fit with Bridgeland's conjecture on the derived autoequivalence group of a complex algebraic K3 surface.

MSC classification

Secondary: 14F05: Sheaves, derived categories of sheaves and related constructions 14J28: $K3$ surfaces and Enriques surfaces 18E30: Derived categories, triangulated categories

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 219 , September 2015 , pp. 1 - 8
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2015

References

[1] Addington, N., New derived symmetries of some hyperkähler varieties, preprint, arXiv:1112.0487v3 [math.AG].Google Scholar
[2] Addington, N. and Aspinwall, P. S., Categories of massless D-branes and del Pezzo surfaces, J. High Energy Phys. 2013, 39 pp. MR 3106123.Google Scholar
[3] Anno, I., Weak representation of tangle categories in algebraic geometry, Ph.D. dissertation, Harvard University, Cambridge, Massachusetts, 2008. MR 2711677.Google Scholar
[4] Bondal, A. I. and Kapranov, M. M., Representable functors, Serre functors, and reconstructions (in Russian), Izv. Ross. Akad. Nauk Ser. Mat. 53 (1989), 1183-1205, 1337; English translation in Math. USSR-Izv. 35 (1990), 519-541. MR 1039961.Google Scholar
[5] Bridgeland, T., Stability conditions on K3 surfaces, Duke Math. J. 141 (2008), 241–291. MR 2376815. DOI 10.1215/S0012-7094-08-14122-5.Google Scholar
[6] Halpern-Leistner, D. and Shipman, I., Autoequivalences of derived categories via geometric invariant theory, preprint, arXiv: 1303.5531v1 [math.AG].Google Scholar
[7] Huybrechts, D., Lectures on K3 surfaces, preprint, http://www.math.uni-bonn.de/ people/huybrech/K3Global.pdf (accessed 10 June, 2015).Google Scholar
[8] Huybrechts, D. and Thomas, R., P-objects and autoequivalences of derived categories, Math. Res. Lett. 13 (2006), 87–98. MR 2200048. DOI 10.4310/MRL.2006.v13.n1.a7.Google Scholar
[9] Meachan, C., Derived autoequivalences of generalised Kummer varieties, to appear in Math. Res. Lett., preprint, arXiv: 1212.5286v4 [math.AG].Google Scholar
[10] Mukai, S., “On the moduli space of bundles on K3 surfaces, I” in Vector Bundles on Algebraic Varieties (Bombay, 1984), Tata Inst. Fund. Res. Stud. Math. 11, Tata Inst. Fund. Res., Bombay, 1987, 341–413. MR 0893604.Google Scholar
[11] Orlov, D. O., Projective bundles, monoidal transformations, and derived categories of coherent sheaves (in Russian), Izv. Ross. Akad. Nauk Ser. Mat. 56 (1992), 852–862; English translation in Russian Acad. Sci. Izv. Math. 41 (1993), 133-141. MR 1208153. DOI 10.1070/IM1993v041n01ABEH002182.Google Scholar
[12] Ploog, D., Groups of autoequivalences of derived categories of smooth projective varieties, Ph.D. dissertation, Universität Bonn, Bonn, Germany, 2005.Google Scholar
[13] Rouquier, R., “Categorification of sl2 and braid groups” in Trends in Representation Theory of Algebras and Related Topics, Contemp. Math. 406, Amer. Math. Soc., Providence, 2006, 137–167. MR 2258045. DOI 10.1090/conm/406/07657.CrossRefGoogle Scholar
[14] Seidel, P. and Thomas, R., Braid group actions on derived categories of coherent sheaves, Duke Math. J. 108 (2001), 37–108. MR 1831820. DOI 10.1215/S0012-7094-01-10812-0.Google Scholar