Numerically Deciding the Arithmetically Cohen-Macaulayness of a Projective Scheme

Abstract

In numerical algebraic geometry, a witness point set W is a key object for performing numerical computations on a projective scheme X of pure dimension d > 0 defined over C. If X is arithmetically Cohen-Macaulay, W can also be used to obtain information about X, such as the initial degree of the ideal generated by X and its Castelnuovo-Mumford regularity. Due to this relationship, we develop a new numerical algebraic geometric test for deciding if X is arithmetically Cohen-Macaulay using points which lie (approximately) on a general curve section C of X. For any curve, we also compute other information such as the arithmetic genus and index of regularity. Several examples are presented showing the effectiveness of this method, even when the ideal of X is unknown.

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Document Details

Document Type
Technical Report
Publication Date
Dec 16, 2014
Accession Number
AD1147262

Entities

People

  • Jonathan D Hauenstein
  • Noah S. Daleo

Organizations

  • North Carolina State University

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algebra
  • Algebraic Geometry
  • Algorithms
  • Applied Mathematics
  • Arithmetic
  • Coefficients
  • Computations
  • Equations
  • Geometry
  • Linear Algebra
  • Mathematics
  • New York
  • Physics
  • Polynomials
  • Three Dimensional
  • Two Dimensional
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Mathematical Modeling and Probability Theory.
  • Regression Analysis.