Title: On the Jets and Resolutions of Codimension-$1$ Foliations
Abstract:We introduce the jet schemes of a holomorphic foliation, and thereby prove an alternate characterisation of simple singularities of codimension-$1$ foliations, independent of any normal form. This lea...We introduce the jet schemes of a holomorphic foliation, and thereby prove an alternate characterisation of simple singularities of codimension-$1$ foliations, independent of any normal form. This leads to an equivalent condition for the existence of a desingularisation in the non-dicritical case. We then prove that such a desingularisation always exists, at least on the level of germs.Read More