scholarly journals Kodaira fibrations and beyond: methods for moduli theory

2017 ◽  
Vol 12 (2) ◽  
pp. 91-174 ◽  
Author(s):  
Fabrizio Catanese
Keyword(s):  
Moduli Theory

scholarly journals Moduli Space of Brody Curves, Energy and Mean Dimension

2008 ◽  
Vol 192 ◽  
pp. 27-58 ◽  
Author(s):  
Masaki Tsukamoto
Keyword(s):  
Complex Plane ◽  
Moduli Space ◽  
Hermitian Manifold ◽  
Value Distribution ◽  
Holomorphic Map ◽  
Infinite Dimensional ◽  
Mean Dimension ◽  
The Mean ◽  
Moduli Theory ◽  
Bounded Derivative

AbstractA Brody curve is a holomorphic map from the complex plane ℂ to a Hermitian manifold with bounded derivative. In this paper we study the value distribution of Brody curves from the viewpoint of moduli theory. The moduli space of Brody curves becomes infinite dimensional in general, and we study its “mean dimension”. We introduce the notion of “mean energy” and show that this can be used to estimate the mean dimension.

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.

scholarly journals New and old results on spherical varieties via moduli theory

2018 ◽  
Vol 328 ◽  
pp. 1299-1352 ◽  
Author(s):  
Roman Avdeev ◽  
Stéphanie Cupit-Foutou
Keyword(s):  
Spherical Varieties ◽  
Moduli Theory

K3 Surfaces

2007 ◽  
Author(s):  
D. Huybrechts
Keyword(s):  
Moduli Spaces ◽  
Special Class ◽  
K3 Surfaces ◽  
Derived Categories ◽  
K3 Surface ◽  
Hodge Structures ◽  
Surface Theory ◽  
Torelli Theorem ◽  
Stable Sheaves ◽  
Moduli Theory

After abelian varieties, K3 surfaces are the second most interesting special class of varieties. These have a rich internal geometry and a highly interesting moduli theory. Paralleling the famous Torelli theorem, results from Mukai and Orlov show that two K3 surfaces have equivalent derived categories precisely when their cohomologies are isomorphic weighing two Hodge structures. Their techniques also give an almost complete description of the cohomological action of the group of autoequivalences of the derived category of a K3 surface. The basic definitions and fundamental facts from K3 surface theory are recalled. As moduli spaces of stable sheaves on K3 surfaces are crucial for the argument, a brief outline of their theory is presented.

Temperature stress for bending beam with different moduli under different constraints

2014 ◽  
Vol 10 (2) ◽  
pp. 163-175
Author(s):  
Wenjuan Yao ◽  
Jiankang Liu
Keyword(s):  
Analytical Solution ◽  
Normal Stress ◽  
Temperature Stress ◽  
Compression Modulus ◽  
Maximum Tensile Stress ◽  
Neutral Axis ◽  
Exploratory Research ◽  
Content Type ◽  
Nonlinear Temperature ◽  
Moduli Theory

Purpose – The purpose of this paper is to solve temperature stress for bending beam with different moduli under different constraints subject to nonlinear temperature. Design/methodology/approach – The equations of neutral axis position, normal stress, and displacement of bending beam with different moduli subjected to nonlinear temperature were derived based on different moduli elasticity theory. Meanwhile, iterative procedure was programmed to solve the nonlinear equations. The analytical solution can return back into the result of the same modulus theory, and the analytical solution was compared with finite element numerical solution. It shows that the analytical model proposed in this paper is reliable to use. Furthermore, the influence of different moduli characteristics on the temperature stress and deformation is discussed. Findings – The mechanical behavior of the bending beam with different moduli subject to nonlinear temperature is quite different from the one that is subjected to force. The bending beam maybe exist two neutral axis, and the reasonable selection of tension modulus and compression modulus can improve the distribution of the normal stress and reduce the maximum tensile stress or the maximum compressive stress. Originality/value – The crack produced by temperature stress will affect the integrity and the durability of the structure. The solution for temperature problem with different moduli theory is rarely reported at home and board. In view of this, this paper will do some exploratory research-temperature stress for bending beam with different moduli.

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