Some finitely generated modules and cohomologies and the Jacobian conjecture (Q2724123)
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scientific article; zbMATH DE number 1615680
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some finitely generated modules and cohomologies and the Jacobian conjecture |
scientific article; zbMATH DE number 1615680 |
Statements
Some finitely generated modules and cohomologies and the Jacobian conjecture (English)
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9 July 2001
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Jacobian conjecture
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differential operator
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primitive polynomial
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monodromy
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finite generated cohomology groups
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The main results of the paper are two conditions equivalent to the famous Jacobian conjecture in two-dimensional complex case. The first one is the condition of finite generatedness of certain modules connected to the differential operator NEWLINE\[NEWLINE L(u)=-f'_yu'_x+f'_xu'_y, NEWLINE\]NEWLINE where \(f\in \mathbb C[x,y]\) is a given polynomial without critical points and \(u\) is a holomorphic function. NEWLINENEWLINENEWLINEThe second result is a similar finite generatedness of certain cohomology groups also connected to a given polynomial.
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