The volume of a surface or orbifold pair
Abstract
A surface pair ( X , C ) (X,C) is a germ of a complex normal surface singularity ( X , 0 ) (X,0) and a sum C = ∑ c i C i C=\sum c_iC_i of curves on X X , with c i ∈ [ 0 , 1 ] ∩ Q c_i\in [0,1]\cap \mathbb {Q} . An orbifold pair has c i = 1 / n i c_i=1/n_i , as intersecting with a small sphere gives a 3 3 -dimensional orbifold ( Σ , γ i , n i ) (\Sigma , \gamma _i,n_i) . There are natural notions of morphism and log cover of surface pairs. We introduce a volume V o l ( X , C ) ∈ Q ≥ 0 Vol(X,C)\in \mathbb {Q}_{\geq 0}
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Geometric and Algebraic Topology
Commutative Algebra and Its Applications
Publication details
- Journal / source
- Contemporary mathematics - American Mathematical Society
- Pages
- 387–409
- Publication date
- 1 January 2026
- Language
- EN