On canonical Fano intrinsic quadrics
We classify all $\mathbb{Q}$-factorial Fano intrinsic quadrics of dimension three and Picard number one having at most canonical singularities.
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arXiv subjects
Christoff Hische
Publications and source records attributed to Christoff Hische.
On Fano threefolds with $\mathbb{C}^*$-action
We study three-dimensional Fano varieties with $\mathbb{C}^*$-action. Complementing recent results [13], we give classification results in the canonical case, where the maximal orbit quotient is $\mathbb{P}_2$ having a line arrangement of five lines in special position as its critical values.
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On the anticanonical complex
The anticanonical complex has been introduced as a natural generalization of the toric Fano polytope and so far has been succesfully used for the study of varieties with a torus action of complexity one. In the present article we enlarge the area of application of the anticanonical complex to varieties with a torus action of higher complexity, for example, general arrangement varieties. As an application of our techniques we classify the three-dimensional canonical Fano intrinsic quadrics with automorphism group having a maximal torus of dimension one.
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On torus actions of higher complexity
We systematically produce algebraic varieties with torus action by constructing them as suitably embedded subvarieties of toric varieties. The resulting varieties admit an explicit treatment in terms of toric geometry and graded ring theory. Our approach extends existing constructions of rational varieties with torus action of complexity one and delivers all Mori dream spaces with torus action. We exhibit the example class of general arrangement varieties and obtain classification results in the case of complexity two and Picard number at most two, extending former work in complexity one.
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