Classifying singularities up to analytic extensions of scalars is smooth
نویسنده
چکیده
The singularity space consists of all germs (X, x), with X a Noetherian scheme and x a point, where we identify two such germs if they become the same after an analytic extension of scalars. This is a Polish space for the metric given by the order to which infinitesimal neighborhoods agree after base change. In other words, the classification of singularities up to analytic extensions of scalars is a smooth problem in the sense of descriptive set-theory.
منابع مشابه
Classifying Singularities up to Analytic Extensions of Scalars
The singularity space consists of all germs (X, x), with X a Noetherian scheme and x a point, where we identify two such germs if they become the same after an analytic extension of scalars. This is a Polish space for the metric given by the order to which infinitesimal neighborhoods agree after base change. In other words, the classification of singularities up to analytic extensions of scalar...
متن کاملCobordisms of Maps with Singularities of a given Class
Let P be a smooth manifold of dimension p. We will describe the group of all cobordism classes of smooth maps of n-dimensional closed manifolds into P with singularities of a given class (including all fold singularities if n ≧ p) in terms of certain stable homotopy groups by applying the homotopy principle on the existence level, which is assumed to hold for those smooth maps. We will also dea...
متن کاملLevi-flat Hypersurfaces with Real Analytic Boundary
Let X be a Stein manifold of dimension at least 3. Given a compact codimension 2 real analytic submanifold M of X, that is the boundary of a compact Levi-flat hypersurface H, we study the regularity of H. Suppose that the CR singularities of M are an O(X)-convex set. For example, suppose M has only finitely many CR singularities, which is a generic condition. Then H must in fact be a real analy...
متن کاملFuchsian analysis of singularities in Gowdy spacetimes beyond analyticity
Fuchsian equations provide a way of constructing large classes of spacetimes whose singularities can be described in detail. In some of the applications of this technique only the analytic case could be handled up to now. This paper develops a method of removing the undesirable hypothesis of analyticity. This is applied to the specific case of the Gowdy spacetimes in order to show that analogue...
متن کاملRecovering exponential accuracy from collocation point values of smooth functions with end-point singularities
Gibbs phenomenon is the particular manner how a global spectral approximation of a piecewise analytic function behaves at the jump discontinuity. The truncated spectral series has large oscillations near the jump, and the overshoot does not decay as the number of terms in the truncated series increases. There is therefore no convergence in the maximum norm, and convergence in smooth regions awa...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Ann. Pure Appl. Logic
دوره 162 شماره
صفحات -
تاریخ انتشار 2011