• GEORG SCHUMACHER

Articles written in Proceedings – Mathematical Sciences

• Line bundles and flat connections

We prove that there are cocompact lattices $\Gamma$ in $\rm SL(2,\mathbb C)$ with the property that there are holomorphic line bundles $L$ on $\rm SL(2,\mathbb C)/ \Gamma$ with $c_{1}(L) = 0$ such that $L$ does not admit any unitary flat connection.

• Symplectic reduction of Sasakian manifolds

When a complex semisimple group $G$ acts holomorphically on a K\"ahler manifold $(X,\, \omega)$ such that a maximal compact subgroup $K\, \subset\, G$ preserves the symplectic form $\omega$, a basic result of symplectic geometry says that the corresponding categorical quotient $X/G$ can be identified with the quotient of the zero-set of the moment map by the action of $K$. We extend this to the context of a semisimple group acting on a Sasakian manifold.

• # Proceedings – Mathematical Sciences

Volume 132, 2022
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Posted on July 25, 2019

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