Category: Algebraic Geometry

Download Riemannsche Flächen by Klaus Lamotke PDF

By Klaus Lamotke

Das vorliegende Buch beruht auf Vorlesungen und Seminaren für Studenten mittlerer und höherer Semester im Anschluß an eine Einführung in die komplexe Funktionentheorie. Die Theorie Riemannscher Flächen wird als ein Mikrokosmos der Reinen Mathematik dargestellt, in dem Methoden der Topologie und Geometrie, der komplexen und reellen research sowie der Algebra zusammenwirken, um die reichhaltige Struktur dieser Flächen aufzuklären und an vielen Beispielen und Bildern zu erläutern, die in der historischen Entwicklung eine Rolle spielten. Wegen seiner Methodenvielfalt enthält es gleichzeitig Einführungen in die Topologie (Fundamentalgruppe, Überlagerungen, Flächen), in die algebraische Geometrie (Kurven und ihre Singularitäten) und in die Potentialtheorie (Perron-Prinzip).
Die 2. Auflage wurde um eine genauere Betrachtung des Kleinschen 14-Ecks, ein Kapitel über die de Rhamsche Cohomologie und einen Paragraphen über die Lösung nicht-linearer Gleichungen der Mathematischen Physik mittels Riemannscher Thetafunktionen ergänzt.

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Download K3 Surfaces and Their Moduli by Carel Faber, Gavril Farkas, Gerard van der Geer PDF

By Carel Faber, Gavril Farkas, Gerard van der Geer

Provides a different and up to date resource at the advancements during this very lively and various field
Connects to different present issues: the research of derived different types and balance stipulations, Gromov-Witten thought, and dynamical systems
Complements comparable volumes like “The Moduli area of Curves” and “Moduli of Abelian kinds” that experience develop into classics

This ebook offers an summary of the newest advancements about the moduli of K3 surfaces. it really is aimed toward algebraic geometers, yet can also be of curiosity to quantity theorists and theoretical physicists, and keeps the culture of comparable volumes like “The Moduli area of Curves” and “Moduli of Abelian Varieties,” which originated from meetings at the islands Texel and Schiermonnikoog and that have develop into classics.

K3 surfaces and their moduli shape a primary subject in algebraic geometry and mathematics geometry, and feature lately attracted loads of recognition from either mathematicians and theoretical physicists. Advances during this box frequently end result from blending subtle options from algebraic geometry, lattice conception, quantity idea, and dynamical platforms. the subject has acquired major impetus as a result of fresh breakthroughs at the Tate conjecture, the examine of balance stipulations and derived different types, and hyperlinks with reflect symmetry and string concept. whilst, the speculation of irreducible holomorphic symplectic forms, the better dimensional analogues of K3 surfaces, has turn into a mainstream subject in algebraic geometry.

Topics
Algebraic Geometry

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Download Period Mappings and Period Domains by James Carlson, Stefan Müller-Stach, Chris Peters PDF

By James Carlson, Stefan Müller-Stach, Chris Peters

The idea that of a interval of an elliptic critical is going again to the 18th century. Later Abel, Gauss, Jacobi, Legendre, Weierstrass and others made a scientific examine of those integrals. Rephrased in smooth terminology, those provide the way to encode how the complicated constitution of a two-torus varies, thereby displaying that yes households include all elliptic curves. Generalizing to better dimensions led to the formula of the distinguished Hodge conjecture, and in an try and remedy this, Griffiths generalized the classical concept of interval matrix and brought interval maps and interval domain names which replicate how the complicated constitution for greater dimensional forms varies. the elemental conception as built via Griffiths is defined within the first a part of the publication. Then, within the moment half spectral sequences and Koszul complexes are brought and are used to derive effects approximately cycles on greater dimensional algebraic forms akin to the Noether-Lefschetz theorem and Nori's theorem. eventually, within the 3rd half differential geometric tools are defined best as much as proofs of Arakelov-type theorems, the theory of the mounted half, the stress theorem, and extra. Higgs bundles and kin to harmonic maps are mentioned, and this results in amazing effects corresponding to the truth that compact quotients of sure interval domain names can by no means admit a Kahler metric or that definite lattices in classical Lie teams cannot happen because the primary team of a Kahler manifold.

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Download Elliptic Curves: Function Theory, Geometry, Arithmetic by Henry McKean, Victor Moll PDF

By Henry McKean, Victor Moll

The topic of elliptic curves is without doubt one of the jewels of nineteenth-century arithmetic, whose masters have been Abel, Gauss, Jacobi, and Legendre. This booklet offers an introductory account of the topic within the sort of the unique discoverers, with references to and reviews approximately newer and sleek advancements. It combines 3 of the elemental subject matters of arithmetic: complicated functionality thought, geometry, and mathematics. After an off-the-cuff preparatory bankruptcy, the e-book follows a historic course, starting with the paintings of Abel and Gauss on elliptic integrals and elliptic capabilities. this can be by way of chapters on theta services, modular teams and modular features, the quintic, the imaginary quadratic box, and on elliptic curves. the numerous routines with tricks scattered during the textual content supply the reader a glimpse of additional advancements. Requiring just a first acquaintance with advanced functionality idea, this e-book is a perfect advent to the topic for graduate scholars and researchers in arithmetic and physics.

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Download p-adic geometry. Lectures from the 2007 Arizona Winter by Matthew Baker, Brian Conrad, Samit Dasgupta, Kiran S. PDF

By Matthew Baker, Brian Conrad, Samit Dasgupta, Kiran S. Kedlaya, Jeremy Teitelbaum, edited by David Savitt, and Dinesh S. Thakur

In fresh a long time, $p$-adic geometry and $p$-adic cohomology theories became critical instruments in quantity conception, algebraic geometry, and the speculation of automorphic representations. The Arizona wintry weather tuition 2007, on which the present e-book is predicated, was once a special chance to introduce graduate scholars to this topic. Following beneficial introductions by means of John Tate and Vladimir Berkovich, pioneers of non-archimedean geometry, Brian Conrad's bankruptcy introduces the final concept of Tate's inflexible analytic areas, Raynaud's view of them because the time-honored fibers of formal schemes, and Berkovich areas. Samit Dasgupta and Jeremy Teitelbaum speak about the $p$-adic higher part airplane to illustrate of a inflexible analytic area and provides purposes to quantity thought (modular types and the $p$-adic Langlands program). Matthew Baker bargains a close dialogue of the Berkovich projective line and $p$-adic strength conception on that and extra normal Berkovich curves. eventually, Kiran Kedlaya discusses theoretical and computational facets of $p$-adic cohomology and the zeta features of types. This ebook can be a welcome boost to the library of any graduate pupil and researcher who's attracted to studying in regards to the suggestions of $p$-adic geometry

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Download Cohomology of quotients in symplectic and algebraic geometry by Frances Clare Kirwan PDF

By Frances Clare Kirwan

These notes describe a basic technique for calculating the Betti numbers of the projective quotient types that geometric invariant idea affiliates to reductive team activities on nonsingular complicated projective forms. those quotient forms are fascinating specifically as a result of their relevance to moduli difficulties in algebraic geometry. the writer describes various methods to the matter. One is solely algebraic, whereas the opposite makes use of the tools of symplectic geometry and Morse idea, and comprises extending classical Morse thought to sure degenerate functions.

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Download Selected topics in algebraic geometry by Virgil Snyder PDF

By Virgil Snyder

This publication resulted from experiences (published in 1928 and 1932) of the Committee on Rational variations, demonstrated through the nationwide learn Council. the aim of the stories used to be to provide a complete survey of the literature at the topic. every one bankruptcy is thought of as a separate unit that may be learn independently.

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Download Basic Algebraic Geometry 2 by Igor R. Shafarevich, Miles Reid PDF

By Igor R. Shafarevich, Miles Reid

Shafarevich's easy Algebraic Geometry has been a vintage and universally used advent to the topic because its first visual appeal over forty years in the past. because the translator writes in a prefatory word, ``For all [advanced undergraduate and starting graduate] scholars, and for the various experts in different branches of math who want a liberal schooling in algebraic geometry, Shafarevich’s e-book is a must.''

The moment quantity is in elements: booklet II is a steady cultural creation to scheme conception, with the 1st target of placing summary algebraic types on an organization origin; a moment goal is to introduce Hilbert schemes and moduli areas, that function parameter areas for different geometric buildings. publication III discusses advanced manifolds and their relation with algebraic forms, Kähler geometry and Hodge concept. the ultimate part raises an vital challenge in uniformising better dimensional forms that has been extensively studied because the ``Shafarevich conjecture''.

The form of  simple Algebraic Geometry 2 and its minimum necessities make it to a wide quantity self sufficient of  uncomplicated Algebraic Geometry 1, and available to starting graduate scholars in arithmetic and in theoretical physics.

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