On codimension 1 del Pezzo foliations on varieties with mild singularities
By Carolina Araujo, S. Druel. 2012
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In this paper we extend to the singular setting the theory of Fano foliations developed in our previous paper (Araujo and Druel, Adv Math 238:70–118, 2013). A $$\mathbb {Q}$$Q-Fano foliation on a complex projective variety $$X$$X is a foliation $$\fancyscript{F}\subsetneq T_X$$F⊊TX whose anti-canonical class $$-K_{\fancyscript{F}}$$-KF is an ample $$\mathbb {Q}$$Q-Cartier divisor. In the spirit of Kobayashi–Ochiai Theorem, we prove that under some conditions the index $$i_{\fancyscript{F}}$$iF of a $$\mathbb {Q}$$Q-Fano foliation is bounded by the rank $$r$$r of $$\fancyscript{F}$$F, and classify the cases in which $$i_{\fancyscript{F}}=r$$iF=r. Next we consider $$\mathbb {Q}$$Q-Fano foliations $$\fancyscript{F}$$F for which $$i_{\fancyscript{F}}=r-1$$iF=r-1. These are called del Pezzo foliations. We classify codimension 1 del Pezzo foliations on mildly singular varieties.
Subfields: Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/51e8dd62de86c92665f0a6178dfa088133353c7b
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In Geometry and Topology
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