The Shi arrangement of the type $D_ell$

In this paper, we give a basis for the derivation module of the cone over the Shi arrangement of the type $D_ell$ explicitly.

$S_t^1times S_s^1$-valued lightcone Gauss map of a Lorentzian surface in semi-Euclidean 4-space

We define the notions of $S_t^1times S_s^1$-valued lightcone Gauss maps, lightcone pedal surface and Lorentzian lightcone height function of Lorentzian surface in semi-Euclidean 4-space and established the relationships between singularities of theseobjects and geometric invariants of the surface as applications of standard techniques of singularity theory for the Lorentzian lightcone height function.