# FFRT Properties of hypersurfaces and their F-signature

## TL;DR

This paper investigates the FFRT properties and F-signatures of specific hypersurfaces in prime characteristic, providing criteria and explicit calculations through matrix factorizations.

## Contribution

It establishes necessary and sufficient conditions for FFRT in certain hypersurfaces and computes their F-signatures using explicit matrix factorizations.

## Key findings

- Identifies conditions for FFRT in hypersurfaces
- Calculates F-signatures explicitly
- Provides new methods for analyzing hypersurface properties

## Abstract

This paper studies properties of certain hypersurfaces in prime characteristic: we give a sufficient and necessary conditions for some classes of such hypersurfaces to have Finite $F$-representation Type (FFRT) and we compute the $F$-signatures of these hypersurfaces. The main method used in this paper is based on finding explicit matrix factorizations.