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Face enumeration for line arrangements in a 2-torus

Authors
  • Chandrasekhar, Karthik1
  • Deshpande, Priyavrat2
  • 1 University of Kentucky, Department of Mathematics, Washington, USA , Washington (United States)
  • 2 Chennai Mathematical Institute, New Delhi, India , New Delhi (India)
Type
Published Article
Journal
Indian Journal of Pure and Applied Mathematics
Publisher
Indian National Science Academy
Publication Date
Sep 07, 2017
Volume
48
Issue
3
Pages
345–362
Identifiers
DOI: 10.1007/s13226-017-0234-7
Source
Springer Nature
Keywords
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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 fi denote the number of i-dimensional faces; these so-called face numbers satisfy the Euler relation ∑i(-1)ifi = 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.

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