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Analytic and Algebraic Geometry - ebook/pdf
Analytic and Algebraic Geometry - ebook/pdf
Autor: , Liczba stron: 205
Wydawca: Wydawnictwo Uniwersytetu Łódzkiego Język publikacji: polski
ISBN: 978-83-7969-243-9 Data wydania:
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Kategoria: ebooki >> naukowe i akademickie >> matematyka
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Annual Conferences in Analytic and Algebraic Geometry have been organized by Faculty of Mathematics and Computer Science of the University of Łódź since 1980. Until now, proceedings of these conferences (mainly in Polish) have comprised educational materials describing current state of a branch of mathematics, new approaches to known topics, and new proofs of known results (http://konfrogi.math.uni.lodz.pl/).

The volume include new results and survey articles concerning real and complex algebraic geometry, singularities of curves and hypersurfaces, invariants of singularities (the Milnor number, degree of C0-sufficiency), algebraic theory of derivations and others topics.

English translation of the Polish version of an article by Stanisław Łojasiewicz (1926-2002) devoted to the famous Hironaka theorem on resolution of singularities. It contains his original approach to the problem in the case of curves and coherent analytic sheaves on 2-dimensional manifolds. This interesting article has not yet been available in English.

The volume is dedicated to the memory of Stanisław Łojasiewicz. We are deeply indebted to him for introducing the topics of analytic and algebraic geometry in the Łódź mathematical centre.

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Tadeusz Krasiński – Department of Algebraic Geometry and Theoretical Computer Science, Faculty of Mathematics and Computer Science, 90-238 Łódź, Banacha Str. 22 krasinski@uni.lodz.pl Stanisław Spodzieja – Department of Analytical Functions and Differential Equations, Faculty of Mathematics and Computer Science, 90-238 Łódź, Banacha Str. 22 spodziej@math.uni.lodz.pl COVER DESIGN Michał M. Jankowski © Copyright by University of Łódź, Łódź 2013 Publication reviewed Printed directly from camera‐ready materials provided to the Łódź University Press by Department of Analytical Functions and Differential Equations First Edition. W.06395.13.0.K ISBN (wersja drukowana) 978-83-7969-017-6 ISBN (ebook) 978-83-7969-243-9 Łódź University Press 90-131 Łódź, ul. Lindleya 8 www.wydawnictwo.uni.lodz.pl e-mail: ksiegarnia@uni.lodz.pl tel. (42) 665 58 63, faks (42) 665 58 62 Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Photography of Stanisław Łojasiewicz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7 Facsimile of one page by Stanisław Łojasiewicz. . . . . . . . . . . . . . . . . . . . . . .9 1. Stanisław Łojasiewicz Geometric desingularization of curves in manifolds . . . . . . . . . . . . . . . . . . 11 2. Szymon Brzostowski, Necessary conditions for irreducibility of algebroid plane curves . . . . 33 3. Evelia Rosa Garc´ıa Barroso and Arkadiusz Płoski, Euclidean algorithm and polynomial equations after Labatie . . . . . . . 41 4. Zbigniew Jelonek, On smooth hypersurfaces containing a given subvariety . . . . . . . . . . . . 51 5. Piotr Jędrzejewicz, Rings of constants of polynomial derivations and p-bases . . . . . . . . . . . 57 6. Grzegorz Oleksik, On combinatorial criteria for isolated singularities . . . . . . . . . . . . . . . . . . 81 7. Beata Osińska-Ulrych, Grzegorz Skalski, Stanisław Spodzieja, On C0-sufficiency of jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .95 8. Arkadiusz Płoski, Introduction to the local theory of plane algebraic curves . . . . . . . . . . 115 9. Jean-Marie Strelcyn, On Chouikha’s isochronicity criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 10. Justyna Walewska, The jump of Milnor numbers in families of non-degenerate and non-convenient singularities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 11. Michał Zakrzewski, Henryk Żołądek, Multiple zeta values and the WKB method . . . . . . . . . . . . . . . . . . . . . . . 155 Preface Annual Conferences in Analytic and Algebraic Geometry have been organized by Faculty of Mathematics and Computer Science of the University of Łódź since 1980. Until now, proceedings of these conferences (mainly in Polish) have comprised educational materials describing current state of a branch of mathematics, new approaches to known topics, and new proofs of known results (see the Internet page: http://konfrogi.math.uni.lodz.pl/). The subject of the present volume include new results and survey articles concer- ning real and complex algebraic geometry, singularities of curves and hypersurfaces, invariants of singularities (the Milnor number, degree of C0-sufficiency), algebraic theory of derivations and others topics. One remarkable element of this collection is an English translation of the Polish version, published in proceedings of the above mentioned conferences, of an article by Stanisław Łojasiewicz (1926-2002) devoted to the famous Hironaka theorem on resolution of singularities. It contains his original approach to the problem in the case of curves and coherent analytic sheaves on 2-dimensional manifolds. This interesting article has not yet been available in English. Additionally, we add a photo portrait of him and the facsimile of one page of his original handwritten manuscript. We would like to thank Arkadiusz Płoski for the help in preparing the volume, Michał Jankowski for designing the cover, referees for preparing reports of the articles and all participants of the Conferences for their good humor and enthusiasm in doing mathematics. Finally, we would like to thank Stanisław Łojasiewicz jr and Anna Ostoja- Łojasiewicz, the heirs of Stanisław Łojasiewicz, for having agreed to include his article into this volume. We dedicate the whole volume to the memory of Stanisław Łojasiewicz. November 2013, Łódź Tadeusz Krasiński Stanisław Spodzieja Stanisław Łojasiewicz (9 X 1926 – 14 XI 2002) (The photo was taken by Przemysław Skibiński in 2000) The facsimile of the first page of the Polish handwritten version of the article (1988) by Stanisław Łojasiewicz, translated in this volume.
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