Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSemi-continuity of the Diederich-Fornaess and Steinness indices
107
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this paper, we prove the semi-continuity theorem of Diederich-Forn{ae}ss index and Steinness index under a smooth deformation of pseudoconvex domains in Stein manifolds.
rate research
Read More
We propose the concept of Diederich--Forn{ae}ss and Steinness indices on compact pseudoconvex CR manifolds of hypersurface type in terms of the DAngelo 1-form. When the CR manifold bounds a domain in a complex manifold, under certain additional non-degeneracy condition, those indices are shown to coincide with the original Diederich--Forn{ae}ss and Steinness indices of the domain, and CR invariance of the original indices follows.
In this short Note we show that the direct image sheaf R 1 $pi$ * (O X) associated to an analytic family of compact complex manifolds $pi$ : X $rightarrow$ S parametrized by a reduced complex space S is a locally free (coherent) sheaf of O S --modules. This result allows to improve a semi-continuity type result for the algebraic dimension of compact complex manifolds in an analytic family given in [B.15]. AMS Classification 2010. 32G05-32A20-32J10.
We introduce the concept of Steinness index related to the Stein neighborhood basis. We then show several results: (1) The existence of Steinness index is equivalent to that of strong Stein neighborhood basis. (2) On the Diederich-Forn{ae}ss worm domains in particular, we present an explicit formula relating the Steinness index to the well-known Diederich-Forn{ae}ss index. (3) The Steinness index is 1 if a smoothly bounded pseudoconvex domain admits finitely many boundary points of infinite type.
We characterize the Diederich-Fornaess index and the Steinness index in terms of a special 1-form, which we call DAngelo 1-form. We then prove that the Diederich-Fornaess and Steinness indices are invariant under CR-diffeomorphisms by showing CR-invariance of DAngelo 1-forms.
For a constructible etale sheaf on a smooth variety of positive characteristic ramified along an effective divisor, the largest slope in Abbes and Saitos ramification theory of the sheaf gives a divisor with rational coefficients called the conductor divisor. In this article, we prove decreasing properties of the conductor divisor after pull-backs. The main ingredient behind is the construction of etale sheaves with pure ramifications. As applications, we first prove a lower semi-continuity property for conductors of etale sheaves on relative curves in the equal characteristic case, which supplement Deligne and Laumons lower semi-continuity property of Swan conductors and is also an $ell$-adic analogue of Andres semi-continuity result of Poincare-Katz ranks for meromorphic connections on complex relative curves. Secondly, we give a ramification bound for the nearby cycle complex of an etale sheaf ramified along the special fiber of a regular scheme semi-stable over an equal characteristic henselian trait, which extends a main result in a joint work with Teyssier and answers a conjecture of Leal in a geometric situation.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
