## Several Complex Variables, Part 1 (Google eBook)Raymond O'Neil Wells, American Mathematical Society |

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### Contents

3 | |

11 | |

Cartesian product structure of singularities | 21 |

Remarks on asymptotic integrals the polynomial of I N Bernstein and | 31 |

Deformations of cusp singularities | 37 |

On n for surface singularities | 45 |

Smoothing perfect varieties | 51 |

The structure of weighted homogeneous polynomials | 57 |

Boundary behaviour of the Caratheodory and Kobayashi metrics | 149 |

A uniqueness theory for the induced CauchyRiemann operator | 157 |

CR structures and their extensions | 169 |

Uniform bounds on derivatives for the 9problem in the polydisk | 177 |

Hyperfunction boundary values and a generalized BochnerHartogs theorem | 187 |

Parametrices for the boundary laplacian and related hypoelliptic differential | 195 |

On the global real analyticity of solutions to D6 on compact manifolds | 205 |

Methods of partial differential equations in complex analysis | 215 |

Deformations of quotient surface singularities | 65 |

Simultaneous resolutions of singularities | 73 |

iii | 84 |

Deformations of coherent analytic sheaves with isolated singularities | 85 |

Local cohomology groups for resolutions of singularities | 91 |

Application of 96 to deformation of isolated singularities | 97 |

The Dirichlet problem for a complex MongeAmpere equation | 109 |

Type conditions for real submanifolds of C | 115 |

Gevrey regularity up to the boundary for the 9 Newmann problem | 123 |

The maximum modulus principle for CR functions on smooth real embedded | 139 |

Compactifying C 241 | 241 |

On the cancellation problem for compact complexanalytic manifolds | 247 |

Differential forms with subanalytic singularities integral cohomology residues | 255 |

On the homotopy type of weighted homogeneous normal complex surfaces | 263 |

Holomorphic vector fields on projective varieties | 273 |

Ldimension and deformations | 285 |

Compact quotients of C3 by affine transformation groups | 293 |

Intermediate Jacobians and the Hodge conjecture for cubic fourfolds | 303 |

Holomorphic chains and their boundaries | 309 |

383 | |

### Common terms and phrases

algebraic Amer American Mathematical Society analytic set assume bidimension biholomorphic bundle chains codimension coefficients cohomology compact support complex analytic complex manifold components condition conjecture coordinates COROLLARY CR functions CR structure curve cusp singularity defined definition deformation denote differential forms differential operators dimension divisor equation equisingular equivalent exists extension fiber finite germs given hence hermitian Hodge conjecture holomorphic functions holomorphic p-chain homogeneous homology hypersurface hypoellipticity implies integral intersection irreducible isolated singularities isomorphism J. J. Kohn kernel Lemma Levi form linear locally flat locally rectifiable Math meromorphic metric Monge-Ampere equation monodromy morphism neighborhood nonsingular obtain open subset plurisubharmonic plurisubharmonic functions polynomial problem projective proof of Theorem PROPOSITION prove pseudoconvex domain real analytic result satisfies sheaf smooth solution Stein subanalytic subject classifications 1970 submanifold subvariety supp Suppose Theorem 3.3 topological unique vector fields Volume 30 zero

### Popular passages

Page 56 - G. Kempf and D. Laksov, The determinantal formula of Schubert calculus, Acta Math. 132 (1974), 153-162.