434 research outputs found
Approximate Hermitian-Yang-Mills structures and semistability for Higgs bundles. II: Higgs sheaves and admissible structures
We study the basic properties of Higgs sheaves over compact K\"ahler
manifolds and we establish some results concerning the notion of semistability;
in particular, we show that any extension of semistable Higgs sheaves with
equal slopes is semistable. Then, we use the flattening theorem to construct a
regularization of any torsion-free Higgs sheaf and we show that it is in fact a
Higgs bundle. Using this, we prove that any Hermitian metric on a
regularization of a torsion-free Higgs sheaf induces an admissible structure on
the Higgs sheaf. Finally, using admissible structures we proved some properties
of semistable Higgs sheaves.Comment: 18 pages; some typos correcte
avelumab anti pd l1 in japanese patients with advanced gastric or gastroesophageal junction cancer gc gejc updated results from the phase ib javelin solid tumour jpn trial
n/
Bergman kernel and complex singularity exponent
We give a precise estimate of the Bergman kernel for the model domain defined
by where
is a holomorphic map from to ,
in terms of the complex singularity exponent of .Comment: to appear in Science in China, a special issue dedicated to Professor
Zhong Tongde's 80th birthda
The Quantum McKay Correspondence for polyhedral singularities
Let G be a polyhedral group, namely a finite subgroup of SO(3). Nakamura's
G-Hilbert scheme provides a preferred Calabi-Yau resolution Y of the polyhedral
singularity C^3/G. The classical McKay correspondence describes the classical
geometry of Y in terms of the representation theory of G. In this paper we
describe the quantum geometry of Y in terms of R, an ADE root system associated
to G. Namely, we give an explicit formula for the Gromov-Witten partition
function of Y as a product over the positive roots of R. In terms of counts of
BPS states (Gopakumar-Vafa invariants), our result can be stated as a
correspondence: each positive root of R corresponds to one half of a genus zero
BPS state. As an application, we use the crepant resolution conjecture to
provide a full prediction for the orbifold Gromov-Witten invariants of [C^3/G].Comment: Introduction rewritten. Issue regarding non-uniqueness of conifold
resolution clarified. Version to appear in Inventione
Characterizing normal crossing hypersurfaces
The objective of this article is to give an effective algebraic
characterization of normal crossing hypersurfaces in complex manifolds. It is
shown that a hypersurface has normal crossings if and only if it is a free
divisor, has a radical Jacobian ideal and a smooth normalization. Using K.
Saito's theory of free divisors, also a characterization in terms of
logarithmic differential forms and vector fields is found and and finally
another one in terms of the logarithmic residue using recent results of M.
Granger and M. Schulze.Comment: v2: typos fixed, final version to appear in Math. Ann.; 24 pages, 2
figure
Laser-Shock Compression and Hugoniot Measurements of Liquid Hydrogen to 55 GPa
The principal Hugoniot for liquid hydrogen was obtained up to 55 GPa under
laser-driven shock loading. Pressure and density of compressed hydrogen were
determined by impedance-matching to a quartz standard. The shock temperature
was independently measured from the brightness of the shock front. Hugoniot
data of hydrogen provide a good benchmark to modern theories of condensed
matter. The initial number density of liquid hydrogen is lower than that for
liquid deuterium, and this results in shock compressed hydrogen having a higher
compression and higher temperature than deuterium at the same shock pressure.Comment: 8 pages, 7 figures, 2 tables, accepted for publication in Physical
Review
Cohomological Hasse principle and motivic cohomology for arithmetic schemes
In 1985 Kazuya Kato formulated a fascinating framework of conjectures which
generalizes the Hasse principle for the Brauer group of a global field to the
so-called cohomological Hasse principle for an arithmetic scheme. In this paper
we prove the prime-to-characteristic part of the cohomological Hasse principle.
We also explain its implications on finiteness of motivic cohomology and
special values of zeta functions.Comment: 47 pages, final versio
Constructions of free commutative integro-differential algebras
In this survey, we outline two recent constructions of free commutative
integro-differential algebras. They are based on the construction of free
commutative Rota-Baxter algebras by mixable shuffles. The first is by
evaluations. The second is by the method of Gr\"obner-Shirshov bases.Comment: arXiv admin note: substantial text overlap with arXiv:1302.004
Clinical significance of VEGF-A, -C and -D expression in esophageal malignancies
Vascular endothelial growth factors ( VEGF)- A, - C and - D are members of the proangiogenic VEGF family of glycoproteins. VEGF-A is known to be the most important angiogenic factor under physiological and pathological conditions, while VEGF-C and VEGF-D are implicated in the development and sprouting of lymphatic vessels, so called lymphangiogenesis. Local tumor progression, lymph node metastases and hematogenous tumor spread are important prognostic factors for esophageal carcinoma ( EC), one of the most lethal malignancies throughout the world. We found solid evidence in the literature that VEGF expression contributes to tumor angiogenesis, tumor progression and lymph node metastasis in esophageal squamous cell carcinoma ( SCC), and many authors could show a prognostic value for VEGF-assessment. In adenocarcinoma (AC) of the esophagus angiogenic properties are acquired in early stages, particularly in precancerous lesions like Barrett's dysplasia. However, VEGF expression fails to give prognostic information in AC of the esophagus. VEGF-C and VEGF-D were detected in SCC and dysplastic lesions, but not in normal mucosa of the esophagus. VEGF-C expression might be associated with lymphatic tumor invasion, lymph node metastases and advanced disease in esophageal SCC and AC. Therapeutic interference with VEGF signaling may prove to be a promising way of anti-angiogenic co-treatment in esophageal carcinoma. However, concrete clinical data are still pending
- …