Projective normality of the wonderful compactification of semisimple adjoint groups (Q1601725)

Let \(G\) be a semisimple adjoint group over an algebraically closed field of arbitrary characteristic. De Concini and Procesi introduced and studied what is called ``the wonderful compactification'' \(X\) of \(G\) [see \textit{C. De Concini} and \textit{C. Procesi}, in: Invariant theory, Proc. 1st 1982 Sess. CIME, Monecatini, Lect. Notes Math. 996, 1-44 (1983; Zbl 0581.14041)]. Let \(\widehat G\) be the simply connected covering of \(G\). The aim of the paper under review is to prove that for every \(\widehat G\times\widehat G\)-linearised very ample line bundle \(L\) over \(X\), the cone over \((X,L)\) is normal.