Seminario prof. Tomasz Szemberg - 8 novembre 2024

L'8 Novembre 2024 alle ore 15:30 in aula 124, il professore Tomasz Szemberg dell’University of the National Educational Commission Krakow - Poland, terrà un seminario dal titolo: "Postulation of lines in $\PP^3$ revisited".

Abstract

 Harbourne and Hirschowitz proved in 1982 that the union $Y$ of general lines in $\PP^3$ has good postulation, i.e., the maps
$$H^0(\PP^3,\calo_{\PP^3}(d))\to H^0(Y,\calo_Y(d))$$ have maximal rank for all $d\geq 1$. Their proof is based on degenerating some of the lines to a ruling on a smooth quadric in $\PP^3$. For this reason, it was considered difficult to generalize their result to higher dimensional projective spaces. We propose a new proof, which does not require degenerations to a smooth quadric but applies rather degeneration to a plane in $\PP^3$. This approach opens door to study postulation of general codimension 2 linear subspaces in higher dimensional projective spaces.