JournalsowrVol. 4 / No. 4DOI 10.4171/owr/2007/47

Komplexe Algebraische Geometrie

  • Gang Tian

    Princeton University, USA
  • Fabrizio Catanese

    Universität Bayreuth, Germany
  • Yujiro Kawamata

    University of Tokyo, Japan
  • Eckart Viehweg

    Universität Duisburg-Essen, Germany
Komplexe Algebraische Geometrie cover

You need to subscribe to download the article.


The Workshop \emph{Komplexe algebraische Geometrie}, organized by Fabrizio Catanese (Bayreuth), Yujiro Kawamata (Tokyo), Gang Tian (Princeton), and Eckart Vieh\-weg (Essen), drew together 50 participants. There were several young PhD students and other PostDocs in their 20's and early 30's, together with established leaders of the fields related to the thematic title of the workshop. There were 23 talks, each lasting 55 minutes or one hour, and each followed by a lively 10 minutes discussion.

As usual at an Oberwolfach Meeting, the mathematical discussions continued outside the lecture room throughout the day and the night. The Conference fully fulfilled its purported aim, of setting in contact mathematicians with different specializations and non uniform background, of presenting new fashionable topics alongside with new insights on long standing classical open problems, and also cross-fertilizations with other research topics as arithmetic and physics. For the latter, cf. the talk by Bernd Siebert on the new approach to Mirror Symmetry through logarithmic geometry and toric affine Calabi Yau varieties and the one by van Straten on quantization of completely integrable Hamiltonian Systems. For the former, cf. the talks by Winkelmann on integral sets and by McQuillan on the Bloch principle.

A central role was occupied by the new results around the Hodge conjecture presented by Voisin, and the new results by Hacon, M\textsuperscript{c}Kernan et al which give an essential step towards the final solution of the Minimal Model Program, and were presented here by M\textsuperscript{c}Kernan with a proposed approach to the Sarkisov program.

There were many expositions dealing with several classical problems and classical and modern theories. It would take too long to dwell on each of the outstanding contributions presented at the Conference. For some topics there were several interrelated talks, for instance we could mention the following classical themes:

\begin{enumerate} \item Abelian Varieties, Jacobian and Prym Varieties and their Moduli spaces (van der Geer, Farkas, Lange, Hulek) \item Hodge Theory and Variation of Hodge structures (Voisin, M\"oller, Barja) \item Fibred varieties (Oguiso, Moeller) \item Algebraic Surfaces (Mukai, Pardini) \item Fundamental groups and algebraic fundamental groups (Esnault, Bauer, Pardini). \end{enumerate}

There were also expositions on many other beautiful topics:

\begin{enumerate} \item Moduli spaces of sheaves on higher dimensional varieties (Lehn) \item Deformations of special complex maifolds (Rollenske) \item Varieties of power sums (Takagi) \item Ball quotients (M\"uller-Stach) \item Stacks and Azumaya algebras (Schr\"oer) \item nefness and vector bundles (Peternell) \end{enumerate}

The variety of striking results and the very interesting and challenging proposals made the participation in the workshop rather strenuous but certainly highly rewarding. We hope that the quality of the expositions in these abstracts will make them quite useful to the mathematical community.