T. Peternell

collaborators

4 papers

math.AG2025

Compactification of homology cells, Fujita's conjectures and the complex projective space

Ping Li, Thomas Peternell

We show that a compact KÃ¤hler manifold $M$ containing a smooth connected divisor $D$ such that $M ∖ D$ is a homology cell, e.g., contractible, must be projective space wit…

math.AG2025

Compactifications of C^n and the complex projective space

Thomas Peternell

We show that the complex projective space is the only projective manifold compactifying $C^{n}$ by a smooth connected hypersurface, provided $n$ is even. In the odd dimensio…

math.AG2024

A contraction theorem for divisors fibering over a curve

Andreas HÃ¶ring, Thomas Peternell

Given a Q-Cartier divisor $S \subset X$ admitting a fibration $S \to B$ onto a curve we give sufficient conditions for the existence of a bimeromorphic contraction contract…

math.AG2024

Klt degenerations of projective spaces

Andreas HÃ¶ring, Thomas Peternell

We study degenerations of complex projective spaces $P^{n}$ into normal projective klt varieties $X$ . If the tangent sheaf of $X$ is semi-stable, we show that $X$ itself is a…