Objective In relation with the study of both moduli and enumerative problems incomplex algebraic geometry, we propose the geometric study of various families of subvarieties ofcertain complex algebraic varieties of small dimension, and mainly offamilies of (possibly singular) curves. The Severi varieties are atypical example: they parametrize curves of given degree and geometricgenus in the projective plane; the general such curve has a prescribednumber of ordinary double points and no further singularity. Apart from exploring their dimensions, smoothness, and irreducibilityproperties, we have in mind to determine their Hilbert polynomials (which among other things encode their degrees, the latter beingimportant enumerative invariants).A central feature of our project is to conduct this analysis bydegeneration: to study families of subvarieties in a given variety X,we let X degenerate and look at what happens in the limit. Forinstance, to study curves on a general K3 surface, we can let itdegenerate to a union of projective planes, the dual graph of which isa triangulation of the real 2-sphere.We shall consider the following kind of families of subvarieties:families of curves with prescribed invariants and singularities insurfaces (with special attention to the two cases of the projective plane,and of K3 surfaces), families of hyperplane sections with prescribedsingularities of hypersurfaces in projective spaces, families ofcurves with a given genus in Calabi-Yau threefolds, and families ofsurfaces in the projective 3-space containing curves with unexpectedsingularities. Fields of science natural sciencesphysical sciencestheoretical physicsstring theorynatural sciencesmathematicspure mathematicsgeometryengineering and technologyenvironmental engineeringenergy and fuelsnatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Programme(s) H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions Main Programme H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility Topic(s) MSCA-IF-2014-EF - Marie Skłodowska-Curie Individual Fellowships (IF-EF) Call for proposal H2020-MSCA-IF-2014 See other projects for this call Funding Scheme MSCA-IF-EF-ST - Standard EF Coordinator UNIVERSITA DEGLI STUDI DI ROMA TOR VERGATA Net EU contribution € 180 277,20 Address VIA CRACOVIA 50 00133 Roma Italy See on map Region Centro (IT) Lazio Roma Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 180 277,20
