##### Department of Mathematics,

University of California San Diego

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### Math 208 - Algebraic Geometry Seminar

## Yi Hu

#### University of Arizona

## Local Resolution of Singularities

##### Abstract:

Mnev's universality theorem asserts that every singularity type over the ring of integers appears in some thin Schubert cell of the Grassmannian Gr(3,E) for some vector space E. We construct sequential blowups of Gr(3,E) such that certain induced birational transforms of all thin Schubert cells become smooth over prime fields. This implies that every singular variety X defined over a prime field admits local resolutions. For a singular variety X over a general perfect field k, we spread it out and deduce that X/k admits local resolution as well.

Host: James McKernan

### November 5, 2021

### 4:00 PM

### Contact Samir Canning at srcannin@ucsd.edu for zoom info.

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