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!

We are grateful for support of German Research council (DFG) through the Emmy-Noether-Programm until 2018 and currently through the research grant Moduli spaces for complex nilmanifolds.

Logo Emmy-Noether-Programm DFG

Publications and Preprints

2022
  • Anh Thi Do and Sönke Rollenske Gorenstein stable surfaces with $K^2_X=1$ and $\chi(\mathcal O_X)=2$. Comm. Algebra 50 (2022), no. 10, 4218–4251.
  • Alex Küronya, Sönke Rollenske, Simple cyclic covers of the plane and Seshadri constants of some general hypersurfaces in weighted projective space Boll. Unione Mat. Ital. 15 (2022), no. 1-2, 269–276. (arxiv) (journal)
  • Marco Franciosi, Rita Pardini, Julie Rana, Sönke Rollenske, I-surfaces with one T-singularity , Boll. Unione Mat. Ital. 15 (2022), no. 1-2, 173–190. (arxiv)
  • Stephen Coughlan, Marco Franciosi, Rita Pardini, Sönke Rollenske, Degeneration of Hodge structures on I-surfaces, (arxiv)
  • Adam Czapliński, Andreas Krug, Manfred Lehn, Sönke Rollenske, Compactified Jacobians of Extended ADE Curves and Lagrangian Fibrations, (arxiv)
  • Nicolina Istrati, Piotr Pokora, Sönke Rollenske, Special triple covers of algebraic surfaces, (arxiv)
2021
2020
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)
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
  • 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)