Butterflies I: Morphisms of 2-group stacks

More on Morphisms of Stacks

More on Morphisms of Stacks

Deformation theory of representable morphisms of algebraic stacks

We study the relationship between the deformation theory of representable 1-morphisms between algebraic stacks and the cotangent complex defined by Laumon and Moret-Bailly.

Relative Dimension of Morphisms and Dimension for Algebraic Stacks

Motivated by applications in moduli theory, we introduce a flexible and powerful language for expressing lower bounds on relative dimension of morphisms of schemes, and more generally of algebraic stacks. We show that the theory is robust and applies to a wide range of situations. Consequently, we obtain simple tools for making dimension-based deformation arguments on moduli spaces. Additionall...

Nonrigid Group Theory of Water Clusters ( Cyclic Forms): (H2O)i for 2<=i<=6

The character table of the fully nonrigid water cluster (cyclic forms), (H_{2}O){_i}, with C{_ih} symmetry derived for the first time, for 2<=i <=6. The group of all feasible permutations is the wreath product of groups S{_i}[S{_2}] which consists of i!2i operations for i = 2, ..., 6 divided into ( w.r.t) 5, 10, 20, 36, 65 conjugacy classes and 5, 10, 20, 36, 65 irreducible representations resp...