## A modular compactification of the general linear group

### Summary

Summary: We define a certain compactifiction of the general linear group and give a modular description for its points with values in arbitrary schemes. This is a first step in the construction of a higher rank generalization of Gieseker's degeneration of moduli spaces of vector bundles over a curve. We show that our compactification has similar properties as the "wonderful compactification" of algebraic groups of adjoint type as studied by de Concini and Procesi. As a byproduct we obtain a modular description of the points of the wonderful compactification of ${PGl}_n$.

### Mathematics Subject Classification

14H60, 14M15, 20G

### Keywords/Phrases

moduli of vector bundles on curves, modular compactification, general linear group