Recognition Problem of Frontal Singularities

Goo Ishikawa

Journal of Singularities
volume 21 (2020), 149-166

Received: 30 April 2018. Received in revised form: 17 August 2018.

DOI: 10.5427/jsing.2020.21i

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Abstract:

A natural class of mappings, frontal mappings, is explained from both geometric and algebraic aspects. Several results on the recognition of frontal singularities, in particular, cuspidal edges, folded umbrellas, swallowtails, Mond singularities, Shcherbak singularities, and their openings are surveyed.

2010 Mathematical Subject Classification:

Primary 57R45; Secondary 58K50, 53A07, 53D12, 53C50

Key words and phrases:

Jacobi ideal, kernel field, Jacobi module, opening, ramification module, Lorentzian manifold

Author(s) information:

Goo Ishikawa
Faculty of Science
Hokkaido University
Sapporo 060-0810, Japan
email: ishikawa@math.sci.hokudai.ac.jp