The Witt group of a smooth complex surface

1987 ◽  
Vol 277 (3) ◽  
pp. 469-481 ◽  
Author(s):  
Fernando Fern�ndez-Carmena
Keyword(s):  
Complex Surface ◽  
Witt Group ◽  
Smooth Complex

scholarly journals Monomial generators of complete planar ideals

2020 ◽  
pp. 2150032
Author(s):  
Maria Alberich-Carramiñana ◽  
Josep Àlvarez Montaner ◽  
Guillem Blanco
Keyword(s):  
Complex Surface ◽  
Integral Closure ◽  
Geometric Method ◽  
Smooth Complex ◽  
Complete Ideal ◽  
Maximal Contact ◽  
The Ideal

We provide an algorithm that computes a set of generators for any complete ideal in a smooth complex surface. More interestingly, these generators admit a presentation as monomials in a set of maximal contact elements associated to the minimal log-resolution of the ideal. Furthermore, the monomial expression given by our method is an equisingularity invariant of the ideal. As an outcome, we provide a geometric method to compute the integral closure of a planar ideal and we apply our algorithm to some families of complete ideals.

Plurisubharmonic functions on a neighborhood of a torus leaf of a certain class of foliations

2019 ◽  
Vol 31 (6) ◽  
pp. 1457-1466
Author(s):  
Takayuki Koike
Keyword(s):  
Line Bundle ◽  
Elliptic Curve ◽  
Positive Curvature ◽  
Complex Surface ◽  
Holomorphic Foliation ◽  
Hermitian Metric ◽  
Plurisubharmonic Functions ◽  
Smooth Complex ◽  
Normal Bundles ◽  
Dynamical Properties

AbstractLet C be a smooth elliptic curve embedded in a smooth complex surface X such that C is a leaf of a suitable holomorphic foliation of X. We investigate the complex analytic properties of a neighborhood of C under some assumptions on the complex dynamical properties of the holonomy function. As an application, we give an example of {(C,X)} in which the line bundle {[C]} is formally flat along C, however it does not admit a {C^{\infty}} Hermitian metric with semi-positive curvature. We also exhibit a family of embeddings of a fixed elliptic curve for which the positivity of normal bundles does not behave in a simple way.

New replica method with plasma polymerized film by glow discharge

1988 ◽  
Vol 46 ◽  
pp. 414-415
Author(s):  
A. Tanaka ◽  
M. Yamaguchi ◽  
T. Hirano
Keyword(s):  
Power Supply ◽  
Plasma Polymerization ◽  
Vacuum Chamber ◽  
Complex Surface ◽  
Replica Method ◽  
Metal Extraction ◽  
High Voltage Power Supply ◽  
Negative Glow ◽  
Hydrocarbon Gas ◽  
Hydrocarbon Molecules

The plasma polymerization replica method and its apparatus have been devised by Tanaka (1-3). We have published several reports on its application: surface replicas of biological and inorganic specimens, replicas of freeze-fractured tissues and metal-extraction replicas with immunocytochemical markers.The apparatus for plasma polymerization consists of a high voltage power supply, a vacuum chamber containing a hydrocarbon gas (naphthalene, methane, ethylene), and electrodes of an anode disk and a cathode of the specimen base. The surface replication by plasma polymerization in negative glow phase on the cathode was carried out by gassing at 0.05-0.1 Torr and glow discharging at 1.5-3 kV D.C. Ionized hydrocarbon molecules diffused into complex surface configurations and deposited as a three-dimensionally polymerized film of 1050 nm in thickness.The resulting film on the complex surface had uniform thickness and showed no granular texture. Since the film was chemically inert, resistant to heat and mecanically strong, it could be treated with almost any organic or inorganic solvents.

scholarly journals Complex Uncertainty of Surface Data Modeling via the Type-2 Fuzzy B-Spline Model

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1054
Author(s):  
Rozaimi Zakaria ◽  
Abd. Fatah Wahab ◽  
Isfarita Ismail ◽  
Mohammad Izat Emir Zulkifly
Keyword(s):  
Complex Surface ◽  
Complex Data ◽  
Fuzzy Data ◽  
Control Points ◽  
B Spline ◽  
Spline Surface ◽  
Data Control ◽  
Surface Data ◽  
Model Complex

This paper discusses the construction of a type-2 fuzzy B-spline model to model complex uncertainty of surface data. To construct this model, the type-2 fuzzy set theory, which includes type-2 fuzzy number concepts and type-2 fuzzy relation, is used to define the complex uncertainty of surface data in type-2 fuzzy data/control points. These type-2 fuzzy data/control points are blended with the B-spline surface function to produce the proposed model, which can be visualized and analyzed further. Various processes, namely fuzzification, type-reduction and defuzzification are defined to achieve a crisp, type-2 fuzzy B-spline surface, representing uncertainty complex surface data. This paper ends with a numerical example of terrain modeling, which shows the effectiveness of handling the uncertainty complex data.

scholarly journals Non Kählerian surfaces with a cycle of rational curves

2021 ◽  
Vol 8 (1) ◽  
pp. 208-222
Author(s):  
Georges Dloussky
Keyword(s):  
Deformation Theory ◽  
Complex Surface ◽  
Rational Curves ◽  
Intersection Form ◽  
Connected Component ◽  
Hirzebruch Surface ◽  
Compact Complex Surface ◽  
A Chain

Abstract Let S be a compact complex surface in class VII0 + containing a cycle of rational curves C = ∑Dj . Let D = C + A be the maximal connected divisor containing C. If there is another connected component of curves C ′ then C ′ is a cycle of rational curves, A = 0 and S is a Inoue-Hirzebruch surface. If there is only one connected component D then each connected component Ai of A is a chain of rational curves which intersects a curve Dj of the cycle and for each curve Dj of the cycle there at most one chain which meets Dj . In other words, we do not prove the existence of curves other those of the cycle C, but if some other curves exist the maximal divisor looks like the maximal divisor of a Kato surface with perhaps missing curves. The proof of this topological result is an application of Donaldson theorem on trivialization of the intersection form and of deformation theory. We apply this result to show that a twisted logarithmic 1-form has a trivial vanishing divisor.

scholarly journals Non-Destructive Fuel Volume Measurements Can Estimate Fine-Scale Biomass across Surface Fuel Types in a Frequently Burned Ecosystem

Fire ◽  
2021 ◽  
Vol 4 (3) ◽  
pp. 36
Author(s):  
Quinn A. Hiers ◽  
E. Louise Loudermilk ◽  
Christie M. Hawley ◽  
J. Kevin Hiers ◽  
Scott Pokswinski ◽  
...  
Keyword(s):  
Bulk Density ◽  
Pinus Palustris ◽  
Field Measurements ◽  
Complex Surface ◽  
Fuel Type ◽  
Field Methods ◽  
Volume Measurements ◽  
Woody Litter ◽  
Non Destructive ◽  
Surface Vegetation

Measuring wildland fuels is at the core of fire science, but many established field methods are not useful for ecosystems characterized by complex surface vegetation. A recently developed sub-meter 3D method applied to southeastern U.S. longleaf pine (Pinus palustris) communities captures critical heterogeneity, but similar to any destructive sampling measurement, it relies on separate plots for calculating loading and consumption. In this study, we investigated how bulk density differed by 10-cm height increments among three dominant fuel types, tested predictions of consumption based on fuel type, height, and volume, and compared this with other field measurements. The bulk density changed with height for the herbaceous and woody litter fuels (p < 0.001), but live woody litter was consistent across heights (p > 0.05). Our models predicted mass well based on volume and height for herbaceous (RSE = 0.00911) and woody litter (RSE = 0.0123), while only volume was used for live woody (R2 = 0.44). These were used to estimate consumption based on our volume-mass predictions, linked pre- and post-fire plots by fuel type, and showed similar results for herbaceous and woody litter when compared to paired plots. This study illustrates an important non-destructive alternative to calculating mass and estimating fuel consumption across vertical volume distributions at fine scales.

scholarly journals COHERENT SYSTEMS AND MODULAR SUBAVRIETIES OF $\mathcal{SU}_C(r)$

2012 ◽  
Vol 23 (04) ◽  
pp. 1250037 ◽  
Author(s):  
MICHELE BOLOGNESI ◽  
SONIA BRIVIO
Keyword(s):  
Moduli Spaces ◽  
Vector Bundles ◽  
Low Rank ◽  
Coherent Systems ◽  
Projective Varieties ◽  
Complex Curve ◽  
Smooth Complex ◽  
Moduli Theory ◽  
Modular Varieties ◽  
Small Genus

Let C be an algebraic smooth complex curve of genus g > 1. The object of this paper is the study of the birational structure of certain moduli spaces of vector bundles and of coherent systems on C and the comparison of different type of notions of stability arising in moduli theory. Notably we show that in certain cases these moduli spaces are birationally equivalent to fibrations over simple projective varieties, whose fibers are GIT quotients (ℙr-1)rg// PGL (r), where r is the rank of the considered vector bundles. This allows us to compare different definitions of (semi-)stability (slope stability, α-stability, GIT stability) for vector bundles, coherent systems and point sets, and derive relations between them. In certain cases of vector bundles of low rank when C has small genus, our construction produces families of classical modular varieties contained in the Coble hypersurfaces.

Smooth Complex Reflectors - An Alternative Approach

1995 ◽  
Author(s):  
J. Chinniah ◽  
M. Dassanayake ◽  
B. Patel
Keyword(s):  
Smooth Complex ◽  
Alternative Approach
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