Spherical subcategories in representation theory arXiv 1502.06838
Joint with Andreas Hochenegger and Martin Kalck.
Discrete derived categories II: The silting pairs CW complex and the stability manifold arXiv 1407.5944
Joint with Nathan Broomhead and David Pauksztello. This article shows the contractibility of the space of stability conditions of discrete-derived categories, using the result of Jon Woolf that the CW complex of silting pairs is a deformation retract of the stability space (arXiv 1407.5986).
Discrete derived categories I: homomorphisms, autoequivalences and t-structures arXiv 1312.5203
Joint with Nathan Broomhead and David Pauksztello.
On autoequivalences of some Calabi-Yau and hyperkähler varieties pdf-file, arXiv 1212.4604.
Int.\ Math.\ Res.\ Notices 22 (2014), 6094--6110
Joint work with Pawel Sosna.
Averaging t-structures and extension closure of aisles pdf-file, arXiv 1208.5691.
Journal of Algebra 394 (2013), 51--78.
Joint work with Nathan Broomhead and David Pauksztello.
Spherical subcategories in algebraic geometry pdf-file, arXiv 1208.4046.
Joint work with Andreas Hochenegger and Martin Kalck.
Fourier-Mukai partners and polarised K3 surfaces pdf-file, arXiv 1206.4558.
In: Arithmetic and Geometry of K3 Surfaces and Calabi-Yau Threefolds (editors L. Razu, M. Schütt, Y. Nui). Fields Institute Communications, Vol.\ 67. Springer, 2013.
Joint work with Klaus Hulek.
A geometric construction of Coxeter-Dynkin diagrams of bimodal singularities pdf-file, arXiv 1102.5024.
Manuscripta Mathematica 140 (2013), 195-212.
Joint work with Wolfgang Ebeling.
Autoequivalencs of toric surfaces pdf-file, arXiv 1010.1717.
Proceedings of the AMS, Vol. 142, Number 4 (2014), 1133-1146.
Joint work with Nathan Broomhead.
Poincare series and Coxeter functors for Fuchsian singularities pdf-file, arXiv 0903.4692.
Advances in Mathematics 225 (2010), 1387-1398.
Joint work with Wolfgang Ebeling. This article introduces a notion of Coxeter element for Fuchsian singularities of higher genus, where the Milnor lattice does not have a root basis anymore. We justify this definition by showing that it generalises earlier results about Poincare series and proceed to lift the Coxeter element to a functor.
Postnikov-stability versus Semistability of Sheaves pdf-file, arXiv 0901.1554.
Asian Journal of Mathematics Vol. 18, No. 2 (2014), 247-262.
Joint with Georg Hein. A sequel to the first article on Postnikov stability. We show that Postnikov-stability encompasses both Giesker and slope semistability, in arbitrary dimension.
McKay correspondence for the Poincare series of Kleinian and Fuchsian singularities pdf-file, arXiv 0809.2738.
Mathematische Annalen 347 (2010), 689-702.
Joint work with Wolfgang Ebeling.
Also see this article by Kajiura, Saito, Takahashi about a different lift of the Milnor lattice of a Kleinian singularity, to a hereditary category (be sure to also look at the appendix by Ueda). And see this paper by the same authors about a lift to a hereditary category of some Fuchsian hypersurface singularities coming from weight systems. Note that the categorical approach of the above article works for a much larger class of Fuchsian singularities.
Postnikov-Stability for Complexes on Curves and Surfaces pdf-file, arXiv 0704.2512.
International Journal of Mathematics 23/2 (2012), 1250048, 20 pages.
Joint work with Georg Hein. Here we provide a new notion of (semi)stability for complexes (or objects in a triangulated category). The starting point is that semistable bundles on a curve always have a non-trivial orthogonal complement in the derived sense. In particular, it is a different type of generalisation that Bridgeland's notion of a stability condition which start from the Harder-Narashiman filtrations.
Equivariant autoequivalences for finite group actions pdf-file arXiv math.0508625.
Advances in Mathematics 216 (2007), 62-74.
This stems from chapter 3 of my thesis but contains major improvements.
If reading the article, it is valuable to also look at section 4 of this paper by Dolgachev.
Groups of autoequivalences of derived categories of smooth projective varieties pdf-file
This is my PhD thesis, handed in January 31, 2005. My supervisor was Daniel Huybrechts.
Fourier-Mukai transforms and stable bundles on elliptic curves pdf-file
Contributions to Algebra and Geometry (Beiträge zur Algebra und Geometrie) Vol. 46, No. 2 (2005), 423-434.
Joint work with Georg Hein (2003). See also Chapter 14 in the book "Abelian Varieties, Theta Functions and the Fourier Transform" by Polishchuk; and see this and this paper by Burban and Kreussler for the case of singular curves.
Every other Hodge isometry of the cohomology of a K3 surface is induced by an autoequivalence of the derived category pdf-file
Unpublished preprint FU Berlin (2002). This material is included in my thesis.
The same argument appeared in the paper "Autoequivalences of Derived Category of A K3 Surface and Monodromy Transformations" by Hosono, Lian, Oguiso and Yau.
Comparing Coxeter functors made from exceptional and spherical objects pdf-file
Joint work with Chris Brav. This is a preprint, feedback is welcome. The first two sections (including the statement and proof of the main theorem) are finished.
Note 12/2012: It is very unlikely that this article will be finished.
How not to hang a picture on a wall — Topology in school pdf-file
This is not mathematical research. I wrote this article because I got positive feedback about my short notes for some Kangaroo sessions .