# Geometry of Smooth Extremal Surfaces

@inproceedings{Brosowsky2021GeometryOS, title={Geometry of Smooth Extremal Surfaces}, author={Anna Brosowsky and Janet Page and Tim Ryan and Karen E. Smith}, year={2021} }

We study the geometry of the smooth projective surfaces that are defined by Frobenius forms, a class of homogenous polynomials in prime characteristic recently shown to have minimal possible F-pure threshold among forms of the same degree. We call these surfaces extremal surfaces, and show that their geometry is reminiscent of the geometry of smooth cubic surfaces, especially non-Frobenius split cubic surfaces of characteristic two, which are examples of extremal surfaces. For example, we show…

## One Citation

Lower Bounds on the F-pure Threshold and Extremal Singularities

- Mathematics
- 2020

. We prove that if f is a reduced homogenous polynomial of degree d , then its F -pure threshold at the unique homogeneous maximal ideal is at least 1 d − 1 . We show, furthermore, that its F -pure…

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