Patricia Klein

ABSTRACT

Frobenius splitting, pioneered by Hochster and Roberts in the 1970s and Mehta and Ramanathan in the 1980s, is a technique in characteristic $p$ commutative algebra and algebraic geometry used to control singularities. In the aughts, Knutson showed that Frobenius splittings of a certain type descend through Gröbner degeneration of a certain type, called geometric vertex decomposition. The primary goal of the talk is to give a partial converse to Knutson’s result. We will see that a Frobenius splitting that compatibly splits both link and deletion of a geometric vertex decomposition can, under an additional hypothesis on the form of the splitting, be lifted to a splitting that compatibly splits the original ideal.

This talk is based on joint work with Emanuela De Negri, Elisa Gorla, Jenna Rajchgot, and Lisa Seccia.