This volume brings together recent, original research and survey articles by leading experts in several fields that include singularity theory, algebraic geometry and commutative algebra. The motivation for this collection comes from the wide-ranging research of the distinguished mathematician, Antonio Campillo, in these and related fields. Besides his influence in the mathematical community stemming from his research, Campillo has also endeavored to promote mathematics and mathematicians’ networking everywhere, especially in Spain, Latin America and Europe. Because of his impressive achievements throughout his career, we dedicate this book to Campillo in honor of his 65th birthday.
Researchers and students from the world-wide, and in particular Latin American and European, communities in singularities, algebraic geometry, commutative algebra, coding theory, and other fields covered in the volume, will have interest in this book.
Table of Content
Preface.- Antonio Campillo: A Portrayal of his Life and Work.- Singularities in Positive Characteristic Equisingularity, Classification, Determinacy: Dedicated to Antonio Campillo on the occasion of his 65th birthday.- Ultrametric spaces of branches on arborescent singularities.- Two points of the boundary of toric geometry.- On the Milnor formula in arbitrary characteristic.- Foliations in the plane uniquely determined by minimal subschemes of its singularities.- Newton transformations and the motivic Milnor fiber of a plane curve.- Nash modification on toric curves.- A recursive formula for the motivic Milnor fiber of a plane curve.- On Hasse–Schmidt derivations: the action of substitution maps.- An introduction to resolution of singularities via the multiplicity.- Platonic Surfaces.- Coverings of rational ruled normal surfaces.- Ulrich bundles on Veronese surfaces.- Multiple structures on smooth on singular varieties.- Smoothness in a family of varieties with dihedral symmetry and the DFT matrix.- The Greedy Algorithm and the Cohen-Macaulay property of rings, graphs and toric projective curves.- Binomial ideals and congruences on $/mathbb{N}^n$.- The $K$-theory of toric schemes over regular rings of mixed characteristic.- On finite and nonfinite generation of associated graded rings of Abhyankar valuations.- Symbolic powers of monomial ideals and Cohen-Macaulay vertex-weighted digraphs.- Asymptotics of reduced algebraic curves over finite fields.- The Poincaré polynomial of a linear code.- The Metric Structure of Linear Codes.- On some properties of $A$ inherited by $C_{b}(X, A)$.- A fractional partial differential equation for theta functions.- On continued fractions.
About the author
Gert-Martin Greuel received his Ph D from the University of Göttingen and ETH Zürich. He later went on to become a distinguished senior professor at the Technical University of Kaiserslautern. He then served as the Editor-in-Chief of zb MATH, director of the Mathematical Research Institute Oberwolfach and Chair of ERCOM (European Research Centres on Mathematics).
Luis Narváez Macarro received his Ph D from the Université Paris 7 and Universidad de Sevilla, where he later became professor. For many years, he served as Director of Algebra at the University of Sevilla as well as Director of the Instituto de Matemáticas de la US (IMUS). He has been actively involved with the Real Sociedad Matemática Española (RSME) as both member of governing board and lead for scientific events.
Sebastià Xambó-Descamps is an Emeritus Full Professor of Information and Coding Theory at the Department of Mathematics of the Universitat Politècnica de Catalunya (UPC). He holds a Ph.D. in Mathematics from the University of Barcelona, and an M.Sc. degree in Mathematics from Brandeis University, USA. He has been Full Professor at the Department of Algebra of the Universidad Complutense of Madrid, President of the Catalan Mathematical Society, Dean of the Faculty of Mathematics and Statistics of the UPC and President of the Spanish Conference of Deans of Mathematics. He has led various R+D+I projects, including the development of the Wiris mathematical platform. Among other productions, he authored “Block Error-Correcting Codes–A Computational Primer” and “Real Spinorial Groups–A Short Mathematical Introduction, ” co-authored ’The Enumerative Theory of Conics after Halphen, ” edited “Enumerative Geometry–Sitges 1987, ” and co-edited “Cosmology, Quantum Vacuum and Zeta Functions”.
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