Contact resolutions of singular Jacobi structures
We study contact resolutions of Jacobi structures which are contact on an open subset. We give several classes of examples, as well as classes for which it cannot exist.
math.DG↗
arXiv subjects
Hichem Lassoued
Publications and source records attributed to Hichem Lassoued.
Symplectic resolutions of the quotient of R^2 by a non-finite symplectic group
We construct smooth symplectic resolutions of the quotient of R^2 under some infinite discrete sub-group of GL_2(R) preserving a log-symplectic structure. This extends from algebraic geometry to smooth real differential geometry the Du Val symplectic resolution of C^2/G, with G \subset SL_2(C) a finite group. The first of these infinite groups is G=Z, identified to triangular matrices with spectrum {1}. Smooth functions on the quotient R^2/G come with a natural Poisson bracket, and R^2/Gis for an arbitrary k \geq 1 set-isomorphic to the real Du Val singular variety A_{2k} = {(x,y,z) \in R^3 , x^2 +y^2= z^{2k}}. We show that each one of the usual minimal resolutions of these Du Val varieties are symplectic resolutions of R^2/G. The same holds for G'=Z \rtimes Z/2Z (identified to triangular matrices with spectrum {\pm 1}), with the upper half of D_{2k+1} playing the role of A_{2k}.
math.DG↗
Dimension preserving resolutions of singularities of Poisson structures
Some Poisson structures do admit resolutions by symplectic manifolds of the same dimension. We give examples and simple conditions under which such resolutions can not exist.
math.DG↗