23 oct 2015 -- 15:30
Aula Dal Passo, Dip. Matematica, Università "Tor Vergata", Roma
Abstract.
It is well known that for minimal surfaces of general type with $q = p_g =1$ the invariant $K^2$ can take values $K^2 = 2,...9$. The fine classification for $K^2 = 2,3$ was achieved some years ago, and it required the development of several tools, in joint works with Ciro Ciliberto and Roberto Pignatelli. Existence for each value of $K^2$ was shown through the work of several authors, which I shall briefly survey. I shall then describe several recent results, obtained with Ingrid Bauer and Davide Frapporti, and then I shall speak on work in progress with Toledo, Stover and Keum on the geometric construction of the case $K^2 = 9$, whose existence was shown by Cartwright and Steger using computer calculations.