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Giovedì 29 Gennaio alle ore 14:15, Alessandro Verra (Roma Tre) terrà il seminario di Geometria dal titolo "On nodal cubic threefolds and the degree of a modular map".
Abstract: The classification of complex, nodal cubic threefolds goes back to Corrado Segre. In the first part of the talk Segre's beautiful description is reviewed, even including some historical remarks. Some applications are also described, like for instance the rationality of some moduli spaces of genus 8 Nikulin surfaces. Then we turn to the last and most beautiful case, often named Segre primal. This is 10-nodal and unique up to projective equivalence. It seems ubiquitous in Algebraic Geometry. In the final part we describe the solution of the following enumerative problem, where the Segre primal appears. Let V be a smooth complex cubic threefold and x a general point of it, then the six lines of V through x are in a quadric cone surface and define six points of the projective line. Let f:V→M be the induced rational map, where M is the moduli space of genus two curves: f is generically finite, what is the degree of f? The latter part is a joint work with Ciro Ciliberto.
Il seminario si svolgerà in presenza nell'aula M3. Per ulteriori informazioni, si può contattare gli organizzatori all'email amos.turchet@uniroma3.it.
