## Abstract

A defining function for a real analytic real hypersurface can be uniquely written as 2 Re(H) + E, where H is holomorphic and E contains no pure terms. We study how H and E change when we perform a local biholo- morphic change of coordinates, or multiply by a unit. One of the main results is necesary and sufficient conditions on the first nonvanishing homogeneous part of E (expanded in terms of H) beyond Eqq that serve as obstructions to writing a defining equation as 2 Re(h) 4+e, where e is independent of h. We also find necessary pluriharmonic obstructions to doing this, which arise from the easier case of attempting to straighten the hypersurface.

Original language | English (US) |
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Pages (from-to) | 71-84 |

Number of pages | 14 |

Journal | Transactions of the American Mathematical Society |

Volume | 295 |

Issue number | 1 |

DOIs | |

State | Published - May 1986 |

## ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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