Ideal closure operations via resolution of singularities in characteristic zero - Peter McDonald скачать в хорошем качестве

Ideal closure operations via resolution of singularities in characteristic zero - Peter McDonald

Title: Ideal closure operations via resolution of singularities in characteristic zero Abstract: An important story in commutative algebra over the past 45 years has been a connection between singularities defined using the Frobenius in characteristic p with those coming out of birational algebraic geometry in characteristic zero via resolution of singularities. However, while these singularities in characteristic p can be studied via tight closure theory, there was no known “closure operation” in characteristic zero whose tight-closure-like properties were derived from such resolutions and their associated vanishing theorems. In this talk, I will introduce such an operation, which we call Koszul-Hironaka (KH) closure, and discuss it’s relationship to tight closure, highlighting their similarities (colon-capturing, a version of the Briancon-Skoda property, etc.) and differences. This is joint work with Neil Epstein, Rebecca R.G., and Karl Schwede.