PDF extension seminar
Speaker: Dr. Cyril Jacob, IIT Bombay
Host: Ronnie Mani Sebastain
Title: The Interpolation Problem on Hirzebruch Surfaces
Time, day and date: 11:30:00 AM – 12:30:00 PM, Thursday, September 17
Venue: Ramanujan Hall
Abstract: The interpolation problem for plane curves on $\mathbb P^2$ has been extensively studied, with the SHGH Conjecture providing a conjectural answer. An analogous interpolation problem for curves on Hirzebruch surfaces $\mathbb F_e=\mathbb P(\mathcal O_{\mathbb P^1}\oplus\mathcal O_{\mathbb P^1}(-e))$ was studied by Antonio Laface, who proposed a conjecture closely related to the SHGH Conjecture. In this talk, we examine versions of the SHGH Conjecture for Hirzebruch surfaces. Finally, we prove this conjecture when the number of very general points satisfies $r\leq e+5$. This is joint work with Ronnie Sebastian.