## Prof. Dr. Roger Bielawski

### Project leader

Leibniz-Universität Hannover

E-mail: bielawski(at)math.uni-hannover.de

Telephone: +49 511 762 2315

Homepage: http://service.ifam.uni-hannover.de/~bie…

## Project

**7**Asymptotic geometry of moduli spaces of curves

## Publications within SPP2026

We represent algebraic curves via commuting matrix polynomials. This allows us to show that the canonical Obata connection on the Hilbert scheme of cohomologically stable twisted rational curves of degree *d* in the ℙ3∖ℙ1 is flat for any *d*≥3.

**Related project(s):****7**Asymptotic geometry of moduli spaces of curves

We investigate the geometry of the Kodaira moduli space* M* of sections of a twistor projection, the normal bundle of which is allowed to jump. In particular, we identify the natural assumptions which guarantee that the Obata connection of the hypercomplex part of *M* extends to a logarithmic connection on *M*.

**Related project(s):****7**Asymptotic geometry of moduli spaces of curves

We describe the natural geometry of Hilbert schemes of curves in projective spaces.

**Related project(s):****7**Asymptotic geometry of moduli spaces of curves