## Nagoya Mathematical Journal

### Spherical functors on the Kummer surface

#### Abstract

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.

#### Article information

Source
Nagoya Math. J., Volume 219 (2015), 1-8.

Dates
Revised: 10 April 2014
Accepted: 12 May 2014
First available in Project Euclid: 20 October 2015

https://projecteuclid.org/euclid.nmj/1445345515

Digital Object Identifier
doi:10.1215/00277630-2891370

Mathematical Reviews number (MathSciNet)
MR3413571

Zentralblatt MATH identifier
1342.14037

#### Citation

Krug, Andreas; Meachan, Ciaran. Spherical functors on the Kummer surface. Nagoya Math. J. 219 (2015), 1--8. doi:10.1215/00277630-2891370. https://projecteuclid.org/euclid.nmj/1445345515

#### References

• [1] N. Addington, New derived symmetries of some hyperkähler varieties, preprint, arXiv:1112.0487v3 [math.AG].
• [2] N. Addington and P. S. Aspinwall, Categories of massless D-branes and del Pezzo surfaces, J. High Energy Phys. 2013, 39 pp.
• [3] I. Anno, Weak representation of tangle categories in algebraic geometry, Ph.D. dissertation, Harvard University, Cambridge, Massachusetts, 2008.
• [4] A. I. Bondal and M. M. Kapranov, 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.
• [5] T. Bridgeland, Stability conditions on $K3$ surfaces, Duke Math. J. 141 (2008), 241–291.
• [6] D. Halpern-Leistner and I. Shipman, Autoequivalences of derived categories via geometric invariant theory, preprint, arXiv:1303.5531v1 [math.AG].
• [7] D. Huybrechts, Lectures on $K3$ surfaces, preprint, http://www.math.uni-bonn.de/people/huybrech/K3Global.pdf (accessed 10 June, 2015).
• [8] D. Huybrechts and R. Thomas, $\mathbb{P}$-objects and autoequivalences of derived categories, Math. Res. Lett. 13 (2006), 87–98.
• [9] C. Meachan, Derived autoequivalences of generalised Kummer varieties, to appear in Math. Res. Lett., preprint, arXiv:1212.5286v4 [math.AG].
• [10] S. Mukai, “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.
• [11] D. O. Orlov, 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.
• [12] D. Ploog, Groups of autoequivalences of derived categories of smooth projective varieties, Ph.D. dissertation, Universität Bonn, Bonn, Germany, 2005.
• [13] R. Rouquier, “Categorification of $\mathfrak{sl}_{2}$ and braid groups” in Trends in Representation Theory of Algebras and Related Topics, Contemp. Math. 406, Amer. Math. Soc., Providence, 2006, 137–167.
• [14] P. Seidel and R. Thomas, Braid group actions on derived categories of coherent sheaves, Duke Math. J. 108 (2001), 37–108.