【报告摘要】We demonstrate the vanishing of the first direct image of the structure sheaf of a normal scheme  X  that is mapped properly and birationally over a regular scheme of any dimension.

Additionally, we present examples in dimensions greater than two of a proper birational morphism from a normal and Cohen-Macaulay scheme to a regular scheme, where the second direct image does not vanish and has isolated support.

【报告人简介】Professor Ishii mainly focuses on algebraic geometry. Her research interest is singularity theory, Arc spaces, Jet schemes, Multiplier ideals. She won many important prizes, such as Saruhashi Prize(1995), Takaoka Municipal Prize(1996), MSJ Algebra Prize(2011), Japan Academy Prize(2011), Imperial Prize(2021).