"Del Pezzo surfaces as Springer fibres for exceptional groups"

We show that simultaneous log resolutions of simply elliptic singularities can be constructed inside suitable stacks of principal bundles over elliptic curves. In particular, we give a direct geometrical construction of del Pezzo surfaces from the corresponding exceptional simple algebraic groups.Comment: This is a re-written version of "From exceptional groups to del Pezzo surfaces and simultaneous log resolutions via principal bundles over elliptic curves". It contains 2 figures. This version corrects one of the figure

Del Pezzo surfaces as Springer fibres for exceptional groups

We show that simultaneous log resolutions of simply elliptic singularities can be constructed inside suitable stacks of principal bundles over elliptic curves. In particular, we give a direct geometrical construction of del Pezzo surfaces from the corresponding exceptional simple algebraic groups

Quantum function algebras as quantum enveloping algebras

Inspired by a result in [Ga], we locate two $k[q,q^{-1}]$-integer forms of $F_q[SL(n+1)]$, along with a presentation by generators and relations, and prove that for $q=1$ they specialize to $U({\mathfrak{h}})$, where ${\mathfrak{h}}$ is the Lie bialgebra of the Poisson Lie group $H$ dual of $SL(n+1)$; moreover, we explain the relation with [loc. cit.]. In sight of this, we prove two PBW-like theorems for $F_q[SL(n+1)]$, both related to the classical PBW theorem for $U({\mathfrak{h}})$.Comment: 27 pages, AMS-TeX C, Version 3.0 - Author's file of the final version, as it appears in the journal printed version, BUT for a formula in Subsec. 3.5 and one in Subsec. 5.2 - six lines after (5.1) - that in this very pre(post)print have been correcte