arXiv subjects

Florian Schrack

Publications and source records attributed to Florian Schrack.

4 recordsLinked to original sources

arXiv2016

Global deformations of certain rational almost homogeneous projective bundles

We study global deformations of certain projective bundles over projective spaces. We show that any projective global deformation of a projective bundle over $\bP^1$ carries the structure of a projective bundle over some projective space. Furthermore, we construct examples in arbitrary dimension $\ge 3$ of almost homogeneous Fano projective bundles over $\bP^2$ which can be globally deformed to non-almost homogeneous manifolds.

math.AG↗

arXiv2014

Extremal contractions of 2-Fano fourfolds

We consider extremal contractions on smooth Fano fourfolds whose second Chern character is positive. We show that such contractions can neither be of fiber type nor contract a divisor to a point.

math.AG↗

arXiv2012

Contact Kaehler Manifolds: Symmetries and Deformations

We study complex compact Kaehler manifolds $X$ carrying a contact structure. If $X$ is almost homogeneous and $b_2(X) \geq 2$, then $X$ is a projectivised tangent bundle (this was known in the projective case even without assumption on the existence of vector fields). We further show that a global projective deformation of the projectivised tangent bundle over a projective space is again of this type unless it is the projectivisation of a special unstable bundle over a projective space. Examples for these bundles are given in any dimension.

math.AG↗

arXiv2011

Algebraic approximation of Kähler threefolds

In the present work, we investigate existence of deformations and algebraic approximability for certain uniruled Kähler threefolds. In the first part, we establish existence of infinitesimal deformations for all conic bundles with relative Picard number one over a non-algebraic compact Kähler surface S and existence of positive-dimensional families of deformations in all but some special cases. In the second part, we study the question of algebraic approximability for projective bundles over S and threefolds bimeromorphic to P_1 x S.

math.AG↗