Enumerative Geometry of Hyperplane Arrangements

Abstract

Systems of polynomial equations arise in a wide range of applications, from statistical economics to robot motion planning. Sometimes it s helpful just to count the number of solutions to the system of equations. In enumerative geometry we count the the number of geometric objects that satisfy a specific system of polynomial constraints. The goal of this project is to count the number of hyperplane arrangements sharing the same combinatorial type that also satisfy a list of geometric conditions. We develop explicit formulas for families of generic hyperplane arrangements in any dimension, as well as for families of pencils in the projective plane.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
May 11, 2012
Accession Number
ADA575879

Entities

People

  • Thomas J. Paul

Organizations

  • United States Naval Academy

Tags

Communities of Interest

  • Air Platforms
  • Autonomy
  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algebraic Geometry
  • Algebraic Topology
  • Complex Numbers
  • Computations
  • Computer Programs
  • Computers
  • Equations
  • Geometry
  • Mathematics
  • Motion Planning
  • Polynomials
  • Real Numbers
  • Robots
  • Social Welfare
  • Topology
  • United States Naval Academy
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Operations Research
  • Regression Analysis.

Technology Areas

  • AI & ML
  • AI & ML - Machine Learning Algorithms
  • Autonomy