Prof. Dr. Daniel Greb - Publications

Databases

My preprints on arXiv. My published papers on MathSciNet (subscription required). My Google Scholar entry.



Publications


PREPRINTS


  • Moduli of K3 families over $\mathbb{P}^1$ and complex-hyperkähler metrics induced by deformed twistor cycles, arXiv:2311.13420
    (with Martin Schwald)

    We answer a question posed independently by Fels-Huckleberry-Wolf and Looijenga concerning the geometric meaning of small deformations of twistor cycles in the K3 period domain. These are shown to induce complex-hyperkähler metrics on members of the families via Penrose's Non-linear Graviton construction. On the way to proving this result, we construct a Hausdorff fine moduli space for families of marked K3 surfaces over smooth rational curves in the K3 period domain. Over an open subset containing all twistor cycles we construct a family of such families, which is a universal small deformation for every twistor family. Whenever possible, we extend the results to higher-dimensional irreducible holomorphic-symplectic manifolds.


  • 1-rational singularities and quotients by reductive groups, arXiv:0901.3539

    This preprint will not be submitted; the results follow easily from those in my later paper ''Rational singularities and quotients by holomorphic group actions'' that appeared in Annali della Scuola Normale Superiore di Pisa; however, the preprint gives an independent and technically simpler proof in the algebraic case and avoids the technical difficulties encountered in the analytic setup.


PEER-REVIEWED PUBLICATIONS



CONFERENCE PROCEEDINGS (invited, without peer review)


Habilitationsschrift


Dissertation




MathSciNet-Reviews


Reviews written by myself for Mathematical Reviews can be found here (subscription required).