Wednesday December 1st, 2021 | |
| Time: | 8:30 PM - 9:30 PM |
| Title: | Asymptotic vanishing of syzygies of algebraic varieties |
| Speaker: | Jinhyung Park, Sogang University |
| Abstract: | |
| About ten years ago, Ein-Lazarsfeld showed the asymptotic nonvanishing theorem of syzygies of algebraic varieties. Their result roughly says that almost all "asymptotic syzygies" of algebraic varieties are nonvanishing, and they conjectured that the remaining "asymptotic syzygies" are vanishing. This suggests that the minimal free resolutions of the graded section rings of line bundles on projective varieties have a uniform asymptotic shape as the positivity of the line bundles grows. In this talk, we confirm Ein-Lazarsfeld's conjecture on vanishing of asymptotic syzygies of algebraic varieties. We first prove the conjecture for the case of products of projective spaces, and then following Raicu's argument, we deduce the general case from this special case. | |