Face enumeration for line arrangements in a 2-torus

Karthik Chandrasekhar () and Priyavrat Deshpande ()
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Karthik Chandrasekhar: University of Kentucky
Priyavrat Deshpande: Chennai Mathematical Institute

Indian Journal of Pure and Applied Mathematics, 2017, vol. 48, issue 3, 345-362

Abstract: Abstract A toric arrangement is a finite collection of codimension-1 subtori in a torus. These subtori stratify the ambient torus into faces of various dimensions. Let f i denote the number of i-dimensional faces; these so-called face numbers satisfy the Euler relation ∑ i (-1) i f i = 0. However, not all tuples of natural numbers satisfying this relation arise as face numbers of some toric arrangement. In this paper we focus on toric arrangements in a 2-dimensional torus and obtain a characterization of their face numbers. In particular we show that the convex hull of these face numbers is a cone.

Keywords: Toric arrangements; face enumerations; f-vector (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s13226-017-0234-7

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