اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدTwo finiteness theorem for $(a,b)$-module
91
0
0.0
(
0
)
تأليف
Daniel Barlet
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We prove the following two results 1. For a proper holomorphic function $ f : X to D$ of a complex manifold $X$ on a disc such that ${df = 0 } subset f^{-1}(0)$, we construct, in a functorial way, for each integer $p$, a geometric (a,b)-module $E^p$ associated to the (filtered) Gauss-Manin connexion of $f$. This first theorem is an existence/finiteness result which shows that geometric (a,b)-modules may be used in global situations. 2. For any regular (a,b)-module $E$ we give an integer $N(E)$, explicitely given from simple invariants of $E$, such that the isomorphism class of $Ebig/b^{N(E)}.E$ determines the isomorphism class of $E$. This second result allows to cut asymptotic expansions (in powers of $b$) of elements of $E$ without loosing any information.
قيم البحث
اقرأ أيضاً
On a complex symplectic manifold we prove a finiteness result for the global sections of solutions of holonomic DQ-modules in two cases: (a) by assuming that there exists a Poisson compactification (b) in the algebraic case. This extends our previous
results in which the symplectic manifold was compact. The main tool is a finiteness theorem for R-constructible sheaves on a real analytic manifold in a non proper situation.
Let $k$ be a field finitely generated over the finite field $mathbb F_p$ of odd characteristic $p$. For any K3 surface $X$ over $k$ we prove that the prime to $p$ component of the cokernel of the natural map $Br(k)to Br(X)$ is finite.
We present a proof of Chows theorem using two results of Errett Bishop retated to volumes and limits of analytic varieties. We think this approach suggested a long time ago in the beautiful book by Gabriel Stolzenberg, is very attractive and easier f
or students and newcomers to understand, also the theory presented here is linked to areas of mathematics that are not usually associated with Chows theorem. Furthermore, Bishops results imply both Chows and Remmert-Steins theorems directly, meaning that this approach is more economic and just as profound as Remmert-Steins proof. At the end of the paper there is a comparison table that explains how Bishops theorems generalize to several complex variables classical results of one complex variable.
The $pi_2$-diffeomorphism finiteness result (cite{FR1,2}, cite{PT}) asserts that the diffeomorphic types of compact $n$-manifolds $M$ with vanishing first and second homotopy groups can be bounded above in terms of $n$, and upper bounds on the absolu
te value of sectional curvature and diameter of $M$. In this paper, we will generalize this $pi_2$-diffeomorphism finiteness by removing the condition that $pi_1(M)=0$ and asserting the diffeomorphism finiteness on the Riemannian universal cover of $M$.
This paper is a survey of finiteness results in hyperkahler geometry. We review some classical theorems by Sullivan, Kollar-Matsusaka, Huybrechts, as well as theorems in the recent literature by Charles, Sawon, and joint results of the author with Ve
rbitsky. We also strengthen a finiteness theorem of the author. These are extended notes of the authors talk during the closing conference of the Simons Semester in the Banach Center in Bc{e}dlewo, Poland.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
