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2019•arXiv (Cornell University)Open access

Equimultiplicity of families of map germs from $\\mathbb{C}^2$ to\n $\\mathbb{C}^3$

Otoniel Nogueira da Silva

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Abstract

In 1971, Zariski proposed some questions in Theory of Singularities. One of\nsuch problems is the so-called, nowadays, Zariski's multiplicity conjecture. In\nthis work, we consider the version of this conjecture for families. We answer\npositively Zariski's multiplicity conjecture for a special class of\nnon-isolated singularities.\n

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In 1971, Zariski proposed some questions in Theory of Singularities. One of\nsuch problems is the so-called, nowadays, Zariski's multiplicity conjecture. In\nthis work, we consider the version of this conjecture for families. We answer\npositively Zariski's multiplicity conjecture for a special class of\nnon-isolated singularities.\n

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Available abstract

In 1971, Zariski proposed some questions in Theory of Singularities. One of\nsuch problems is the so-called, nowadays, Zariski's multiplicity conjecture. In\nthis work, we consider the version of this conjecture for families. We answer\npositively Zariski's multiplicity conjecture for a special class of\nnon-isolated singularities.\n

Key concepts: Conjecture, Gravitational singularity, Multiplicity (mathematics), Mathematics, Class (philosophy), Pure mathematics, Combinatorics, Computer science

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