We are mostly interested in the geometry of algebraic varieties and complex manifolds. Some more specific topic we have worked on include the following.

  • Classification of complex and algebraic surfaces
  • Geometry of semi-log-canonical surfaces and the moduli space of stable surfaces
  • Geometry of non-Kähler manifolds, especially left-invariant geometric structures on nilmanifolds
  • Holomorphic symplectic manifolds and Lagrangian fibrations and their non-Kähler analogs
  • Algebraic properties of the sheaf of Kähler differentials

If you want to know more, write an email or come to our seminars!

Our research was supported by the Emmy-Noether-Programm of the German Research council until 2018.

Logo Emmy-Noether-Programm DFG

Publications and Preprints

2021
  • Sönke Rollenske, Virus infections, Corona surfaces,and extra components in the moduli space of stable surfaces (arxiv)
2020
  • Alex Küronya, Sönke Rollenske, Simple cyclic covers of the plane and Seshadri constants of some general hypersurfaces in weighted projective space (arxiv)
  • Marco Franciosi, Rita Pardini, Julie Rana, Sönke Rollenske, I-surfaces with one T-singularity , (arxiv)
2019
  • Anna Fino, Sönke Rollenske, and Jean Ruppenthal, Dolbeault cohomology of complex nilmanifolds foliated in toroidal groups, The Quarterly Journal Of Mathematics ,Volume 70, Issue 4, December 2019, 1265–1279.(arxiv)
  • Sönke Rollenske, Adriano Tomassini, and Xu Wang. Vertical-horizontal decomposition of Laplacians and cohomologies of manifolds with trivial tangent bundles. Annali di Matematica Pura ed Applicata (2019), online first.
2018
  • Marco Franciosi, Rita Pardini, Sönke Rollenske, (p,d)-elliptic curves of genus two., Arkiv för Matematik, Vol. 56, No. 2 (2018), pp. 299–317. (arxiv)
  • Ben Anthes, Andrea Cattaneo, Sönke Rollenske, and Adriano Tomassini, deldelbar-complex symplectic and Calabi–Yau manifolds: Albanese map, deformations and period maps, Ann. Global Anal. Geom., 54(3):377–398, 2018. (arxiv)
  • Ilka Agricola, Giovanni Bazzoni, Oliver Goertsches, Panagiotis Konstantis, and Sönke Rollenske. On the history of the Hopf problem. Differential Geom. Appl., 57:1–9, 2018.
  • Christian Lehn, Sönke Rollenske, and Caren Schinko, The complex geometry of a hypothetical complex structure on S^6, Differential Geom. Appl., 57:121–137, 2018.
  • Marco Franciosi, Sönke Rollenske, Canonical rings of Gorenstein stable Godeaux surfaces , Boll. Unione Mat. Ital., 11(1):75–91, 2018. (Journal) (arxiv)
  • Marco Franciosi, Rita Pardini, Sönke Rollenske, Gorenstein stable Godeaux surfaces, Selecta Math. (N.S.), 24(4):3349–3379, 2018. (Journal) (arxiv)
2017
  • Ju A Lee, Michael Lönne, and Sönke Rollenske, Double Kodaira fibrations with small signature , preprint 2017 (arxiv)
  • Marco Franciosi, Rita Pardini, Sönke Rollenske, Gorenstein stable surfaces with $K_X^2 = 1$ and $p_g>0$., Math. Nach. (2017). (Journal) (arxiv)
2016
  • Sönke Rollenske, A new irreducible component of the moduli space of stable Godeaux surfaces Manuscripta Math. 149 (2016), no. 1-2, 117–130. (Journal) (arxiv)
  • Wenfei Liu, Sönke Rollenske: Geography of Gorenstein stable log surfaces,, Trans. Amer. Math. Soc. 368 (2016), no. 4, 2563–2588. (Journal) (arxiv)
2015
  • Marco Franciosi, Rita Pardini, Sönke Rollenske, Log-canonical pairs and Gorenstein stable surfaces with $K_X^2=1$, Compos. Math. 151 (2015), no. 8, 1529–1542. (journal) (arxiv)
  • Marco Franciosi, Rita Pardini, Sönke Rollenske, Computing invariants of semi-log-canonical surfaces, Math. Z. 280 (2015), no. 3-4, 1107–1123. (Journal) (arxiv)
  • Giovanni Bazzoni, Oliver Goertsches, K-cosymplectic manifolds, Ann. Global Anal. Geom. 47 (2015), no. 3, 239–270. (arxiv)
  • (Journal)
2014
  • Giovanni Bazzoni, Juan Carlos Marrero, Locally conformal symplectic nilmanifolds with no locally conformal Kähler metrics (arxiv)
  • Giovanni Bazzoni, Vicente Muñoz, Manifolds which are complex and symplectic but not Kähler (arxiv)
  • Wenfei Liu, Sönke Rollenske: Pluricanonical maps of stable log surfaces, Adv. Math. 258 (2014), 69–126. (arxiv)
  • (Journal)
  • Laura Bigalke und Sönke Rollenske: Erratum to: The Frölicher spectral sequence can be arbitrarily non-degenerate, Math. Ann., Volume 358, Issue 3-4, pp 1119-1123, 2014. (Journal)
  • Christian Lehn, Daniel Greb und Sönke Rollenske: Lagrangian fibrations on hyperkähler fourfolds,Izvestiya: Mathematics, Volume 78(1), 22-33, 2014. (Journal) (arxiv)
2013
  • Christian Lehn, Daniel Greb und Sönke Rollenske: Lagrangian fibrations on hyperkähler manifolds - On a question of Beauville, Ann. Sci. ENS 46(3), 2013. (Journal)
  • Wenfei Liu, Sönke Rollenske: Geography of Gorenstein stable log surfaces, erscheint in TAMS, (arxiv)
2012
  • Jin-Xing Cai, Wenfei Liu, Lei Zhang: Automorphisms of surfaces of general type with q>=2 acting trivially in cohomology, 2012, (arxiv)
  • Fabrizio Catanese, Wenfei Liu, Roberto Pignatelli: The moduli space of even surfaces of general type with K^2=8, p_g=4 and q=0, 2012, (arxiv)
  • Wenfei Liu: Stable degenerations of surfaces isogenous to a product II, Trans. Amer. Math. Soc. 364 (2012), 2411-2427 (Journal)
  • Markus Zowislok: On moduli spaces of sheaves on K3 or abelian surfaces, Math. Zeit. 272, (3-4), 1195-1217, 2012. (Journal)
  • Wenfei Liu, Sönke Rollenske: Two-dimensional semi-log-canonical hypersurfaces, Le Matematiche, Vol.67 (2), 2012. (pdf)
2011
  • Daniel Greb, Sönke Rollenske: Torsion and cotorsion in the sheaf of Kähler differentials on some mild singularities, Math. Res. Lett. 18, no. 6, 1259–1269, 2011. (Journal)
  • Oliver Goertsches, Sönke Rollenske: Torsion in equivariant cohomology and Cohen-Macaulay G-actions,Transformation Groups, Volume 16, Nummer 4, 1063-1080, 2011. (arxiv), (The original publication is available at www.springerlink.com.)
  • Sönke Rollenske: The computation of the number of connected components, Appendix to Matteo Penegini, Surfaces isogenous to a product with p_g=q=2, Collectanea Math. 62 (3), 2011. (Journal)
  • Sönke Rollenske: Dolbeault cohomology of nilmanifolds with left-invariant complex structure, Complex and Differential Geometry, Conference held at   Leibniz Universität Hannover, September 14 – 18, 2009, vol. 8 of Springer Proceedings in Mathematics, Springer, 2011. (pdf)
  • Sönke Rollenske: The Kuranishi space of complex parallelisable nilmanifolds,   Journal of the European Mathematical Society,  13 (3), 513–531, 2011.  (pdf)
2010
  • Sönke Rollenske: Compact Moduli for certain Kodaira Fibrations,  Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. IX (2010), 851-874. (pdf)
2009
  • Sönke Rollenske, Richard P. Thomas: Smoothing nodal Calabi-Yau n-folds, J. Topology 2, 405-421, 2009. (pdf)
  • Sönke Rollenske: Geometry of nilmanifolds with left-invariant complex structure and deformations in the large, Proc. London Math. Soc., 99, 425-460, 2009. (pdf)
  • Sönke Rollenske: Lie-algebra dolbeault cohomology and small deformations of nilmanifolds, J. London Math. Soc., 79(2), 346-362, 2009. (pdf)
  • Fabrizio Catanese, Sönke Rollenske: Double Kodaira Fibrations, J. Reine Angew. Math. 628, 205-233, 2009. (pdf)
2008 & 2007
  • Sönke Rollenske: The Frölicher spectral sequence can be arbitrarily non degenerate, Math. Ann., 341(3), 623-628, 2008. (pdf)
    (The original publication is available at www.springerlink.com.)
  • Sönke Rollenske: Q.E.D. for Kodaira surfaces, Appendix to Fabrizio Catanese,   Q.E.D. for algebraic varieties, J. Differential Geom., 77(1), 43-75, 2007. (pdf)
Theses of Sönke Rollenske
  • Diplomarbeit Holomorphe Zusammenhange und flache Strukturen auf holomorphen Vektorbündeln , Universität zu Kön, 2005, supervised by Prof. D. Huybrechts. (pdf)
  • Dissertation Nilmanifolds: complex structures, geometry and deformations, Universität Bayreuth, 2007, supervised by Prof. F. Catanese. (pdf)