Department of Mathematics and Computer ScienceEmory University
Cite this article as:
Ojanguren, M. & Parimala, R. manuscripta math. (2009) 130: 387. doi:10.1007/s00229-009-0295-y
Let k be an algebraically closed field. Let P(X11, . . . , Xnn, T) be the characteristic polynomial of the generic matrix (Xij) over k. We determine its singular locus as well as the singular locus of its Galois splitting. If X is a smooth quasi-projective surface over k and A an Azumaya algebra on X of degree n, using a method suggested by M. Artin, we construct finite smooth splittings for A of degree n over X whose Galois closures are smooth.