TY - JOUR

T1 - Defining equations for real analytic real hypersurfaces in Cn

AU - D’Angelo, John P.

PY - 1986/5

Y1 - 1986/5

N2 - 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.

AB - 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.

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U2 - 10.1090/S0002-9947-1986-0831189-5

DO - 10.1090/S0002-9947-1986-0831189-5

M3 - Article

AN - SCOPUS:84968468393

VL - 295

SP - 71

EP - 84

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 1

ER -