Nodal rational sextics in the real projective plane

Diplôme Thèse Nodal rational sextics in the real projective plane eng 2018-02-22 author Josi Johannes 808094 director Mikhalkin Grigory 681622 director Itenberg Ilia 862634 10.13097/archive-ouverte/unige:104672 urn:nbn:ch:unige-1046721 Sc. 5188 This thesis studies nodal sextics (algebraic curves of degree six), and in particular rational sextics, in the real projective plane. Two such sextics with k nodes are callled rigidly isotopic if they can be joined by a path in the space of real nodal sextics with k nodes. The main result of the first part of the thesis is a rigid isotopy classification of real nodal sextics without real nodes, generalizing Nikulin's classification of non-singular sextics. In the second part we study sextics with real nodes and we describe the rigid isotopy classes of such sextics in the case where the sextics are dividing, i.e., their real part separates the complexifcation (the set of complex points) into two halves. As a main application, we give a rigid isotopy classification for those nodal real rational sextics which can be perturbed to maximal or next-to-maximal sextics in the sense of Harnack's inequality. Real algebraic curve Rigid isotopy K3 surface Period map Dewey 510 25 Section de mathématiques 11 false 9faa5b66-cfe7-4f08-a336-aefd9e57d44e Thesis Public these_josi_unige.pdf 1624494 application/pdf Restricted 2018-11-25 05d5f6465d91dbf231d4b918cbfa8ec1aefd9dcce14db7fdef28c541bcf93bb3 openAccess Faculté des sciences / Section de mathématiques

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Nodal rational sextics in the real projective plane				2018	773	660

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Josi, Johannes