
neverendingbooksgeometry (2)
Here pdffiles of older NeverEndingBooksposts on geometry. For more recent posts go here.

lulu neverendingbooks
Half a year ago, it all started with NeverEndingBooks in which I set out a rather modest goal : Why NeverEndingBooks ? We all complain about exaggerated prices of mathematical books from certain publishers, poor quality of editing and refereeing offered, as well as far too stringent bookcontracts. Rather than lamenting about this, NeverEndingBooks gives…

hyperresolutions
[Last time][1] we saw that for $A$ a smooth order with center $R$ the BrauerSeveri variety $X_A$ is a smooth variety and we have a projective morphism $X_A \rightarrow \mathbf{max}~R$ This situation is very similar to that of a desingularization $~X \rightarrow \mathbf{max}~R$ of the (possibly singular) variety $~\mathbf{max}~R$. The top variety $~X$ is a…

smooth BrauerSeveris
Around the same time Michel Van den Bergh introduced his BrauerSeveri schemes, [Claudio Procesi][1] (extending earlier work of [Bill Schelter][2]) introduced smooth orders as those orders $A$ in a central simple algebra $\Sigma$ (of dimension $n^2$) such that their representation variety $\mathbf{trep}_n~A$ is a smooth variety. Many interesting orders are smooth : hereditary orders, trace…

BrauerSeveri varieties
![][1] Classical BrauerSeveri varieties can be described either as twisted forms of projective space (Severi\’s way) or as varieties containing splitting information about central simple algebras (Brauer\’s way). If $K$ is a field with separable closure $\overline{K}$, the first approach asks for projective varieties $X$ defined over $K$ such that over the separable closure $X(\overline{K})…