Cr Singularities of Real Threefolds in C
نویسندگان
چکیده
CR singularities of real threefolds in C4 are classified by using holomorphic coordinate changes to transform the quadratic part of the real defining equations into one of a list of normal forms. In the non-degenerate case, it is shown that a real analytic manifold near a CR singular point is formally equivalent to a real algebraic model. Some degenerate cases also have this property.
منابع مشابه
Addendum To: Cr Singularities of Real Threefolds in C
y2 = E2(z1, z̄1, x2) = O(3) (7.1) z3 = z̄ 1 + e3(z1, z̄1, x2) z4 = (z1 + εx2)z̄1 + e4(z1, z̄1, x2). with ε either 1 or 0, corresponding to whetherM satisfies the second non-degeneracy condition (type (I)) or not (type (II)). To see what transformations will be available to normalize some higher degree terms, we will find the group of transformations which leaves (7.1) invariant. We start with transf...
متن کاملCr Singularities of Real Fourfolds in C
CR singularities of real 4-submanifolds in complex 3-space are classified by using local holomorphic coordinate changes to transform the quadratic coefficients of the real analytic defining equation into a normal form. The quadratic coefficients determine an intersection index, which appears in global enumerative formulas for CR singularities of compact submanifolds.
متن کاملReal Algebraic Threefolds I. Terminal Singularities
In real algebraic geometry, considerable attention has been paid to the study of real algebraic curves (in connection with Hilbert’s 16th problem) and also to real algebraic surfaces. See [Viro90], [Riesler93] and the references there. In higher dimensions one of the main avenues of investigation was initiated by [Nash52], and later developed by many others (see [AK92] for some recent direction...
متن کاملReal Algebraic Threefolds Ii. Minimal Model Program
In real algebraic geometry, one of the main directions of investigation is the topological study of the set of real solutions of algebraic equations. The first general result was proved in [Nash52], and later developed by many others (see [Akbulut-King92] for some recent directions). One of these theorems says that every compact differentiable manifold can be realized as the set of real points ...
متن کاملBoundedness of Fano Threefolds with Log-terminal Singularities of given Index
We prove that all Fano threefolds with log-terminal singularities of given index belong to finitely many families. This result was previously obtained by the author in the case of unipolar Fano varieties. [email protected]
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005