1,966 research outputs found
Finite Generation of Canonical Ring by Analytic Method
In the 80th birthday conference for Professor LU Qikeng in June 2006 I gave a
talk on the analytic approach to the finite generation of the canonical ring
for a compact complex algebraic manifold of general type. This article is my
contribution to the proceedings of that conference from my talk. In this
article I give an overview of the analytic proof and focus on explaining how
the analytic method handles the problem of infinite number of interminable
blow-ups in the intuitive approach to prove the finite generation of the
canonical ring. The proceedings of the LU Qikeng conference will appear as
Issue No. 4 of Volume 51 of Science in China Series A: Mathematics
(www.springer.com/math/applications/journal/11425)
Effective algebraic degeneracy
We prove that any nonconstant entire holomorphic curve from the complex line
C into a projective algebraic hypersurface X = X^n in P^{n+1}(C) of arbitrary
dimension n (at least 2) must be algebraically degenerate provided X is generic
if its degree d = deg(X) satisfies the effective lower bound: d larger than or
equal to n^{{(n+1)}^{n+5}}
Banach Analytic Sets and a Non-Linear Version of the Levi Extension Theorem
We prove a certain non-linear version of the Levi extension theorem for
meromorphic functions. This means that the meromorphic function in question is
supposed to be extendable along a sequence of complex curves, which are
arbitrary, not necessarily straight lines. Moreover, these curves are not
supposed to belong to any finite dimensional analytic family. The conclusion of
our theorem is that nevertheless the function in question meromorphically
extends along an (infinite dimensional) analytic family of complex curves and
its domain of existence is a pinched domain filled in by this analytic family.Comment: 19 pages, This is the final version with significant corrections and
improvements. To appear in Arkiv f\"or matemati
Bilateral Anterior Shoulder Dislocation
Introduction: Unilateral anterior shoulder dislocation is one of the most common problems encountered in orthopedic practice. However, simultaneous bilateral anterior dislocation of the shoulders is quite rare.
Case Presentation: We report a case of a 75-year-old woman presented with simultaneous bilateral anterior shoulder dislocation following a trauma, complicated with a traction injury to the posterior cord of the brachial plexus.
Conclusions: Bilateral anterior shoulder dislocation is very rare. The excessive traction force during closed reduction may lead to nerve palsy. Clear documentation of neurovascular status and adequate imaging before and after a reduction should be performed
The range of the tangential Cauchy-Riemann system on a CR embedded manifold
We prove that every compact, pseudoconvex, orientable, CR manifold of \C^n,
bounds a complex manifold in the sense. In particular, the
tangential Cauchy-Riemann system has closed range
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Capital Requirements and Optimal Investment with Solvency Probability Constraints
Quantifying economic capital and optimally allocating it into portfolios of financial instruments are two key topics in the asset–liability management of an insurance company. In general, these problems are studied in the literature by minimizing standard risk measures such as the value at risk and the conditional VaR. Motivated by Solvency II regulations, we introduce a novel optimization problem to solve for the optimal required capital and the portfolio structure simultaneously, when the ruin probability is used as an insurance solvency constraint. Besides the generic optimal required capital and portfolio problem formulation, we propose a two-model hierarchy of optimization models, where both models admit the so-called second-order conic reformulation, in turn making them particularly well suited for numerics. The first model, albeit naively asserting the normality of the returns on assets and liabilities, under minor further simplifications admits a closed-form solution—a set of formulas, which may be used as simple decision-making guidelines in the analysis of more complex scenarios. A potentially more realistic second model aims to represent the ‘heavy-tailed’ nature of an insurer's liabilities more accurately, while also allowing arbitrary distributions of asset returns via a semi-parametric approach. Extensive numerical simulations illustrate the sensitivity and robustness of the proposed approach relative to the model's parameters. In addition, we explore the potential of insurance risk diversification and discuss if combining several liabilities into a single insurance portfolio may always be beneficial for the insurer. Finally, we propose an extension of the model with an expected return on capital constraint added
Section Extension from Hyperbolic Geometry of Punctured Disk and Holomorphic Family of Flat Bundles
The construction of sections of bundles with prescribed jet values plays a
fundamental role in problems of algebraic and complex geometry. When the jet
values are prescribed on a positive dimensional subvariety, it is handled by
theorems of Ohsawa-Takegoshi type which give extension of line bundle valued
square-integrable top-degree holomorphic forms from the fiber at the origin of
a family of complex manifolds over the open unit 1-disk when the curvature of
the metric of line bundle is semipositive. We prove here an extension result
when the curvature of the line bundle is only semipositive on each fiber with
negativity on the total space assumed bounded from below and the connection of
the metric locally bounded, if a square-integrable extension is known to be
possible over a double point at the origin. It is a Hensel-lemma-type result
analogous to Artin's application of the generalized implicit function theorem
to the theory of obstruction in deformation theory. The motivation is the need
in the abundance conjecture to construct pluricanonical sections from flatly
twisted pluricanonical sections. We also give here a new approach to the
original theorem of Ohsawa-Takegoshi by using the hyperbolic geometry of the
punctured open unit 1-disk to reduce the original theorem of Ohsawa-Takegoshi
to a simple application of the standard method of constructing holomorphic
functions by solving the d-bar equation with cut-off functions and additional
blowup weight functions
Local syzygies of multiplier ideals
In recent years, multiplier ideals have found many applications in local and
global algebraic geometry. Because of their importance, there has been some
interest in the question of which ideals on a smooth complex variety can be
realized as multiplier ideals. Other than integral closure no local
obstructions have been known up to now, and in dimension two it was established
by Favre-Jonsson and Lipman-Watanabe that any integrally closed ideal is
locally a multiplier ideal. We prove the somewhat unexpected result that
multiplier ideals in fact satisfy some rather strong algebraic properties
involving higher syzygies. It follows that in dimensions three and higher,
multiplier ideals are very special among all integrally closed ideals.Comment: 8 page
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