Tomasz Szemberg:
Interpolation on subspaces
Zeit und Ort
Freitag, 25.5.12, 10:00-11:00, Raum 404, Eckerstr. 1
Zusammenfassung
Let P1,...Pr be points in the projective space \bP^n and let m1,...,mr be positive integer. If n=2, then the conjecture of Segre, Harbourne, Gimigliano, Hirschowitz predicts that if the points are general, then the scheme Z=m1P1+...+mrPr either imposes independent conditions on linear systems of curves of degree d, or this system has a non-reduced base curve. For higher n, even the conjectural picture is less clear. On the other hand, a celebrated result of Alexander and Hirschowitz says, that if m1,...,mr are fixed, then the conditions imposed\nby Z on hypersurfaces of degree d are independent, provided d is sufficiently large. There is no reason to restrict imposing conditions only to points. Hartshorne and Hirschowitz studied the postulation problem for a set of general lines in \bP^n. They showed that lines behave as\npoints, i.e. general lines impose independent conditions on\nhypersurfaces. The proof of this result is pretty involved.\nWe study the problem more generally, asking for conditions\nimposed by general configurations of linear subspaces and allowing multiplicities.\n\nThis is work in progress, joint with Brian Harbourne, Marcin Dumnicki, Joaquim Roe and Halszka Tutaj-Gasinska.\n