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Lectures on Curves on an Algebraic Surface

Lectures on Curves on an Algebraic Surface
Author: David Mumford
Publisher: Princeton University Press
Total Pages: 224
Release: 1966-08-21
Genre: Mathematics
ISBN: 9780691079936

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These lectures, delivered by Professor Mumford at Harvard in 1963-1964, are devoted to a study of properties of families of algebraic curves, on a non-singular projective algebraic curve defined over an algebraically closed field of arbitrary characteristic. The methods and techniques of Grothendieck, which have so changed the character of algebraic geometry in recent years, are used systematically throughout. Thus the classical material is presented from a new viewpoint.


Lectures on Curves on an Algebraic Surface. (AM-59), Volume 59

Lectures on Curves on an Algebraic Surface. (AM-59), Volume 59
Author: David Mumford
Publisher: Princeton University Press
Total Pages: 212
Release: 2016-03-02
Genre: Mathematics
ISBN: 1400882060

Download Lectures on Curves on an Algebraic Surface. (AM-59), Volume 59 Book in PDF, ePub and Kindle

These lectures, delivered by Professor Mumford at Harvard in 1963-1964, are devoted to a study of properties of families of algebraic curves, on a non-singular projective algebraic curve defined over an algebraically closed field of arbitrary characteristic. The methods and techniques of Grothendieck, which have so changed the character of algebraic geometry in recent years, are used systematically throughout. Thus the classical material is presented from a new viewpoint.


Introduction to the Theory of Schemes

Introduction to the Theory of Schemes
Author: Yuri I. Manin
Publisher: Springer
Total Pages: 205
Release: 2018-05-15
Genre: Mathematics
ISBN: 3319743163

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This English edition of Yuri I. Manin's well-received lecture notes provides a concise but extremely lucid exposition of the basics of algebraic geometry and sheaf theory. The lectures were originally held in Moscow in the late 1960s, and the corresponding preprints were widely circulated among Russian mathematicians. This book will be of interest to students majoring in algebraic geometry and theoretical physics (high energy physics, solid body, astrophysics) as well as to researchers and scholars in these areas. "This is an excellent introduction to the basics of Grothendieck's theory of schemes; the very best first reading about the subject that I am aware of. I would heartily recommend every grad student who wants to study algebraic geometry to read it prior to reading more advanced textbooks."- Alexander Beilinson


Continuous Model Theory. (AM-58), Volume 58

Continuous Model Theory. (AM-58), Volume 58
Author: Chen Chung Chang
Publisher: Princeton University Press
Total Pages: 165
Release: 2016-03-02
Genre: Mathematics
ISBN: 1400882052

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This is a study of the theory of models with truth values in a compact Hausdorff topological space.


Singularities of Plane Curves

Singularities of Plane Curves
Author: Eduardo Casas-Alvero
Publisher: Cambridge University Press
Total Pages: 363
Release: 2000-08-31
Genre: Mathematics
ISBN: 0521789591

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Comprehensive and self-contained exposition of singularities of plane curves, including new, previously unpublished results.


Arithmetic Moduli of Elliptic Curves. (AM-108), Volume 108

Arithmetic Moduli of Elliptic Curves. (AM-108), Volume 108
Author: Nicholas M. Katz
Publisher: Princeton University Press
Total Pages: 528
Release: 2016-03-02
Genre: Mathematics
ISBN: 1400881714

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This work is a comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces. The arithmetic study of the moduli spaces began with Jacobi's "Fundamenta Nova" in 1829, and the modern theory was erected by Eichler-Shimura, Igusa, and Deligne-Rapoport. In the past decade mathematicians have made further substantial progress in the field. This book gives a complete account of that progress, including not only the work of the authors, but also that of Deligne and Drinfeld.


Geometric Invariant Theory for Polarized Curves

Geometric Invariant Theory for Polarized Curves
Author: Gilberto Bini
Publisher: Springer
Total Pages: 217
Release: 2014-11-07
Genre: Mathematics
ISBN: 3319113372

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We investigate GIT quotients of polarized curves. More specifically, we study the GIT problem for the Hilbert and Chow schemes of curves of degree d and genus g in a projective space of dimension d-g, as d decreases with respect to g. We prove that the first three values of d at which the GIT quotients change are given by d=a(2g-2) where a=2, 3.5, 4. We show that, for a>4, L. Caporaso's results hold true for both Hilbert and Chow semistability. If 3.5a


Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88

Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88
Author: Robion C. Kirby
Publisher: Princeton University Press
Total Pages: 368
Release: 2016-03-02
Genre: Mathematics
ISBN: 1400881501

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Since Poincaré's time, topologists have been most concerned with three species of manifold. The most primitive of these--the TOP manifolds--remained rather mysterious until 1968, when Kirby discovered his now famous torus unfurling device. A period of rapid progress with TOP manifolds ensued, including, in 1969, Siebenmann's refutation of the Hauptvermutung and the Triangulation Conjecture. Here is the first connected account of Kirby's and Siebenmann's basic research in this area. The five sections of this book are introduced by three articles by the authors that initially appeared between 1968 and 1970. Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.