2011/04/21 by Hussein Mourtada, Mourtada, Hussein
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.1104.4297
24 pages, 1 figure
arxiv created 2011/04/21 · arxiv updated 2011/04/22
For m∈ ℕ, m≥ 1, we determine the irreducible components of the m-th jet scheme of a normal toric surface S. We give formulas for the number of these components and their dimensions. When m varies, these components give rise to projective systems, to which we associate a weighted graph. We prove that the data of this graph is equivalent to the data of the analytical type of S. Besides, we classify these irreducible components by an integer invariant that we call index of speciality. We prove that for m large enough, the set of components with index of speciality 1, is in 1-1 correspondance with the set of exceptional divisors that appear on the minimal resolution of S.