Institut für Algebraische Geometrie

Welfengarten 1

30167 Hannover

Telefon: +49 511.762 - 17331

E-mail: ploog@math.uni-hannover.de

**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 .