On Degenerations of the Projective Plane
Complementing results of Hacking and Prokhorov, we determine in an explicit manner all log terminal, rational, degenerations of the projective plane that allow a non-trivial torus action.
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arXiv subjects
Jürgen Hausen
Publications and source records attributed to Jürgen Hausen.
K*-surfaces of Picard number one and integral degree
We give an explicit description of all quasismooth, rational, projective surfaces of Picard number one that admit a non-trivial torus action and have an integral canonical self intersection number.
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Full intrinsic quadrics of dimension two
A full intrinsic quadric is a normal complete variety with a finitely generated Cox ring defined by a single quadratic relation of full rank. We describe all surfaces of this type explicitly via local Gorenstein indices. As applications, we present upper and lower bounds in terms of the Gorenstein index for the degree, the log canonicity and the Picard index. Moreover, we determine all full intrinsic quadric surfaces admitting a Kähler-Einstein metric.
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Log del Pezzo $\mathbb{C}^*$-surfaces, Kähler-Einstein metrics, Kähler-Ricci solitons and Sasaki-Einstein metrics
We consider two classes of non-toric log del Pezzo $\mathbb{C}^*$-surfaces: on the one side the 1/3-log canonical ones and on the other side those of Picard number one and Gorenstein index at most 65. In each of the two classes we figure out the surfaces admitting a Kähler-Einstein metric, a Kähler-Ricci soliton and those allowing a Sasaki-Einstein metric on the link of their anticanonical cone. We encounter examples that admit a Kähler-Ricci soliton but no Sasaki-Einstein cone link metric.
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On Gorenstein Fano Threefolds with an Action of a Two-Dimensional Torus
We classify the non-toric, $\mathbb Q$-factorial, Gorenstein, log terminal Fano threefolds of Picard number one that admit an effective action of a two-dimensional algebraic torus.
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