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Ebook Analytic and algebraic geometry 1

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Opis treści

Annual Conferences in Analytic and Algebraic Geometry have been organized by Facul-ty 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 alge-braic geometry, singularities of curves and hypersurfaces, invariants of singularities (the Milnor number, degree of C0-suﬃciency), algebraic theory of derivations and oth-ers 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 con-tains 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 in-debted to him for introducing the topics of analytic and algebraic geometry in the Łódź mathematical centre.

Spis treści ebooka Analytic and algebraic geometry 1

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 Garcia 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