Ph.D in Mathematics
Junior Seminar "Coincident root loci and the moduli space of rational elliptic surfaces" Simone Pesatori (dottorando matematica, Università Roma Tre)
19/04/2023 - 14:00
Abstract: Elliptic fibrations are strongly characterised by their singular fibers. We analyse the moduli spaces of elliptic surfaces over the projective line P1 and construct a stratification of these spaces in terms of the singular fibers that the surfaces have. In order to do that, we need to investigate a very natural problem: let Pd be the space parametrising homogeneous degree d polynomials in two variables; what happens if the roots of the polynomials collapse? Given a partition ? of d, how is the locus in Pd corresponding to polynomials having roots with the multiplicities prescribed by ??