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Lectures on resolution of singularities
Author:
ISBN: 0691129231 0691129223 9786612157745 1282157744 1400827809 9781400827800 9780691129228 9780691129235 Year: 2007 Publisher: Princeton, N.J. : Princeton University Press,

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Abstract

Resolution of singularities is a powerful and frequently used tool in algebraic geometry. In this book, János Kollár provides a comprehensive treatment of the characteristic 0 case. He describes more than a dozen proofs for curves, many based on the original papers of Newton, Riemann, and Noether. Kollár goes back to the original sources and presents them in a modern context. He addresses three methods for surfaces, and gives a self-contained and entirely elementary proof of a strong and functorial resolution in all dimensions. Based on a series of lectures at Princeton University and written in an informal yet lucid style, this book is aimed at readers who are interested in both the historical roots of the modern methods and in a simple and transparent proof of this important theorem.

Keywords

Singularities (Mathematics) --- 512.761 --- Geometry, Algebraic --- Singularities. Singular points of algebraic varieties --- 512.761 Singularities. Singular points of algebraic varieties --- Adjunction formula. --- Algebraic closure. --- Algebraic geometry. --- Algebraic space. --- Algebraic surface. --- Algebraic variety. --- Approximation. --- Asymptotic analysis. --- Automorphism. --- Bernhard Riemann. --- Big O notation. --- Birational geometry. --- C0. --- Canonical singularity. --- Codimension. --- Cohomology. --- Commutative algebra. --- Complex analysis. --- Complex manifold. --- Computability. --- Continuous function. --- Coordinate system. --- Diagram (category theory). --- Differential geometry of surfaces. --- Dimension. --- Divisor. --- Du Val singularity. --- Dual graph. --- Embedding. --- Equation. --- Equivalence relation. --- Euclidean algorithm. --- Factorization. --- Functor. --- General position. --- Generic point. --- Geometric genus. --- Geometry. --- Hyperplane. --- Hypersurface. --- Integral domain. --- Intersection (set theory). --- Intersection number (graph theory). --- Intersection theory. --- Irreducible component. --- Isolated singularity. --- Laurent series. --- Line bundle. --- Linear space (geometry). --- Linear subspace. --- Mathematical induction. --- Mathematics. --- Maximal ideal. --- Morphism. --- Newton polygon. --- Noetherian ring. --- Noetherian. --- Open problem. --- Open set. --- P-adic number. --- Pairwise. --- Parametric equation. --- Partial derivative. --- Plane curve. --- Polynomial. --- Power series. --- Principal ideal. --- Principalization (algebra). --- Projective space. --- Projective variety. --- Proper morphism. --- Puiseux series. --- Quasi-projective variety. --- Rational function. --- Regular local ring. --- Resolution of singularities. --- Riemann surface. --- Ring theory. --- Ruler. --- Scientific notation. --- Sheaf (mathematics). --- Singularity theory. --- Smooth morphism. --- Smoothness. --- Special case. --- Subring. --- Summation. --- Surjective function. --- Tangent cone. --- Tangent space. --- Tangent. --- Taylor series. --- Theorem. --- Topology. --- Toric variety. --- Transversal (geometry). --- Variable (mathematics). --- Weierstrass preparation theorem. --- Weierstrass theorem. --- Zero set. --- Differential geometry. Global analysis


Book
Complexity in Economic and Social Systems
Authors: --- ---
Year: 2021 Publisher: Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute

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There is no term that better describes the essential features of human society than complexity. On various levels, from the decision-making processes of individuals, through to the interactions between individuals leading to the spontaneous formation of groups and social hierarchies, up to the collective, herding processes that reshape whole societies, all these features share the property of irreducibility, i.e., they require a holistic, multi-level approach formed by researchers from different disciplines. This Special Issue aims to collect research studies that, by exploiting the latest advances in physics, economics, complex networks, and data science, make a step towards understanding these economic and social systems. The majority of submissions are devoted to financial market analysis and modeling, including the stock and cryptocurrency markets in the COVID-19 pandemic, systemic risk quantification and control, wealth condensation, the innovation-related performance of companies, and more. Looking more at societies, there are papers that deal with regional development, land speculation, and the-fake news-fighting strategies, the issues which are of central interest in contemporary society. On top of this, one of the contributions proposes a new, improved complexity measure.

Keywords

volatility clustering --- Baidu Index --- information demand --- generalized autoregressive conditional heteroscedasticity model (GARCH) --- mixture of distribution hypothesis --- speculation --- land acquisition --- motivation --- real estate --- development --- Ethiopia --- systemic risk --- macroprudential policy --- agent-based modelling --- inequality --- central-banking --- information transfer --- transfer entropy --- stock markets --- econophysics --- complexity science --- information theory --- economic complexity --- evolutionary dynamics --- network theory --- leveraged trading --- stock price crash risk --- threshold effect --- complexity in stock market --- entropy economics --- non-extensive cross-entropy econometrics --- non-ergodic ill-behaved inverse problems --- general system theory --- non-linear dynamics --- complex adaptive systems --- homo oeconomicus --- edge of chaos --- complexity economics --- pricing constraint --- IPO timing --- dynamic game model --- real option --- complexity of IPOs --- financial institution --- complex network --- jump volatility --- entropy weight TOPSIS --- structural entropy --- stock market --- EMD --- cluster-entropy --- Shannon-entropy --- financial markets --- time series --- dynamics --- Tsallis entropy --- copula functions --- cross-shareholding network --- finance --- cryptocurrencies --- multivariate transfer entropy --- complex networks --- liquidity proxy --- liquidity benchmark --- volatility estimate --- correlation coefficient --- partial determination --- mutual information --- forecasting market risk --- value at risk --- extreme returns --- peaks over threshold --- self-exciting point process --- discrete-time models --- generalized Pareto distribution --- dynamical complexity --- universal complexity measure --- irreversible processes --- entropies --- entropic susceptibilities --- complex systems --- multifractal analysis --- detrended cross-correlations --- minimal spanning tree --- wealth condensation --- agent-based computational economics --- bargaining --- gain function --- macroeconomics --- innovative activity --- manufacturing industry --- conjunctural movements --- cybernetics --- feedback loops --- correspondence analysis --- Polish Green Island effect --- Red Queen effect --- Kondratieff waves --- power law --- Zipf law --- gender productivity gap --- fake news --- rumor spreading --- Nash equilibrium --- evolutionarily stable strategies --- evolutionary information search dynamics --- nonlinear dynamics --- chaos --- time series analysis --- stock exchange market --- Lyapunov --- recurrence plots --- BDS --- correlation dimension --- GARCH model --- measure of economic development --- websites --- public administration sector --- municipality --- four-colour theorem --- prosumption --- platforms for participation --- location quotient --- dual graph --- Euler characteristic --- n/a

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