Download or read book Algebraic Surfaces In Positive Characteristics Purely Inseparable Phenomena In Curves And Surfaces written by Masayoshi Miyanishi and published by World Scientific. This book was released on 2020-06-29 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Customarily, the framework of algebraic geometry has been worked over an algebraically closed field of characteristic zero, say, over the complex number field. However, over a field of positive characteristics, many unpredictable phenomena arise where analyses will lead to further developments.In the present book, we consider first the forms of the affine line or the additive group, classification of such forms and detailed analysis. The forms of the affine line considered over the function field of an algebraic curve define the algebraic surfaces with fibrations by curves with moving singularities. These fibrations are investigated via the Mordell-Weil groups, which are originally introduced for elliptic fibrations.This is the first book which explains the phenomena arising from purely inseparable coverings and Artin-Schreier coverings. In most cases, the base surfaces are rational, hence the covering surfaces are unirational. There exists a vast, unexplored world of unirational surfaces. In this book, we explain the Frobenius sandwiches as examples of unirational surfaces.Rational double points in positive characteristics are treated in detail with concrete computations. These kinds of computations are not found in current literature. Readers, by following the computations line after line, will not only understand the peculiar phenomena in positive characteristics, but also understand what are crucial in computations. This type of experience will lead the readers to find the unsolved problems by themselves.
Download or read book Affine Algebraic Geometry Geometry Of Polynomial Rings written by Masayoshi Miyanishi and published by World Scientific. This book was released on 2023-12-05 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic geometry is more advanced with the completeness condition for projective or complete varieties. Many geometric properties are well described by the finiteness or the vanishing of sheaf cohomologies on such varieties. For non-complete varieties like affine algebraic varieties, sheaf cohomology does not work well and research progress used to be slow, although affine spaces and polynomial rings are fundamental building blocks of algebraic geometry. Progress was rapid since the Abhyankar-Moh-Suzuki Theorem of embedded affine line was proved, and logarithmic geometry was introduced by Iitaka and Kawamata.Readers will find the book covers vast basic material on an extremely rigorous level:
Download or read book Algebraic Surfaces written by Oscar Zariski and published by Springer. This book was released on 1971 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "The author's book [ ] saw its first edition in 1935. [ ] Now as before, the original text of the book is an excellent source for an interested reader to study the methods of classical algebraic geometry, and to find the great old results. [ ] a timelessly beautiful pearl in the cultural heritage of mathematics as a whole." Zentralblatt MATH
Download or read book Lectures on Curves on an Algebraic Surface AM 59 Volume 59 written by David Mumford and published by Princeton University Press. This book was released on 2016-03-02 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Real Algebraic Surfaces written by Robert Silhol and published by Springer. This book was released on 2006-11-14 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebraic Surfaces written by Lucian Silvestru Badescu and published by . This book was released on 2014-01-15 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebraic Surfaces written by Lucian Badescu and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents fundamentals from the theory of algebraic surfaces, including areas such as rational singularities of surfaces and their relation with Grothendieck duality theory, numerical criteria for contractibility of curves on an algebraic surface, and the problem of minimal models of surfaces. In fact, the classification of surfaces is the main scope of this book and the author presents the approach developed by Mumford and Bombieri. Chapters also cover the Zariski decomposition of effective divisors and graded algebras.
Download or read book Zariski Surfaces and Differential Equations in Characteristic P written by Piotr Blass and published by CRC Press. This book was released on 2020-11-25 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents the current (1985) state of knowledge about Zariski surfaces and related topics in differential equations in characteristic p > 0. It is aimed at research mathematicians and graduate and advanced undergraduate students of mathematics and computer science.
Download or read book Mathematical Reviews written by and published by . This book was released on 2003-05 with total page 870 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Annual Report written by Cornell University. Department of Mathematics and published by . This book was released on 1988 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on K3 Surfaces written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2016-09-26 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi–Yau manifolds from various perspectives in eighteen self-contained chapters. It starts with the basics and guides the reader to recent breakthroughs, such as the proof of the Tate conjecture for K3 surfaces and structural results on Chow groups. Powerful general techniques are introduced to study the many facets of K3 surfaces, including arithmetic, homological, and differential geometric aspects. In this context, the book covers Hodge structures, moduli spaces, periods, derived categories, birational techniques, Chow rings, and deformation theory. Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin–Tate, are discussed in general and for K3 surfaces in particular, and each chapter ends with questions and open problems. Based on lectures at the advanced graduate level, this book is suitable for courses and as a reference for researchers.
Download or read book Enriques Surfaces I written by F. Cossec and published by Nelson Thornes. This book was released on 1989 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of two volumes representing the current state of knowledge about Enriques surfaces which occupy one of the classes in the classification of algebraic surfaces. Recent improvements in our understanding of algebraic surfaces over fields of positive characteristic allowed us to approach the subject from a completely geometric point of view although heavily relying on algebraic methods. Some of the techniques presented in this book can be applied to the study of algebraic surfaces of other types. We hope that it will make this book of particular interest to a wider range of research mathematicians and graduate students. Acknowledgements. The undertaking of this project was made possible by the support of several institutions. Our mutual cooperation began at the University of Warwick and the Max Planck Institute of Mathematics in 1982/83. Most of the work in this volume was done during the visit of the first author at the University of Michigan in 1984-1986. The second author was supported during all these years by grants from the National Science Foundation.
Download or read book The Geometry of Moduli Spaces of Sheaves written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2010-05-27 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.
Download or read book 3264 and All That written by David Eisenbud and published by Cambridge University Press. This book was released on 2016-04-14 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: 3264, the mathematical solution to a question concerning geometric figures.
Download or read book The Geometry of Schemes written by David Eisenbud and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.
Download or read book Classical Algebraic Geometry written by Igor V. Dolgachev and published by Cambridge University Press. This book was released on 2012-08-16 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic geometry has benefited enormously from the powerful general machinery developed in the latter half of the twentieth century. The cost has been that much of the research of previous generations is in a language unintelligible to modern workers, in particular, the rich legacy of classical algebraic geometry, such as plane algebraic curves of low degree, special algebraic surfaces, theta functions, Cremona transformations, the theory of apolarity and the geometry of lines in projective spaces. The author's contemporary approach makes this legacy accessible to modern algebraic geometers and to others who are interested in applying classical results. The vast bibliography of over 600 references is complemented by an array of exercises that extend or exemplify results given in the book.
Download or read book Mordell Weil Lattices written by Matthias Schütt and published by Springer Nature. This book was released on 2019-10-17 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book lays out the theory of Mordell–Weil lattices, a very powerful and influential tool at the crossroads of algebraic geometry and number theory, which offers many fruitful connections to other areas of mathematics. The book presents all the ingredients entering into the theory of Mordell–Weil lattices in detail, notably, relevant portions of lattice theory, elliptic curves, and algebraic surfaces. After defining Mordell–Weil lattices, the authors provide several applications in depth. They start with the classification of rational elliptic surfaces. Then a useful connection with Galois representations is discussed. By developing the notion of excellent families, the authors are able to design many Galois representations with given Galois groups such as the Weyl groups of E6, E7 and E8. They also explain a connection to the classical topic of the 27 lines on a cubic surface. Two chapters deal with elliptic K3 surfaces, a pulsating area of recent research activity which highlights many central properties of Mordell–Weil lattices. Finally, the book turns to the rank problem—one of the key motivations for the introduction of Mordell–Weil lattices. The authors present the state of the art of the rank problem for elliptic curves both over Q and over C(t) and work out applications to the sphere packing problem. Throughout, the book includes many instructive examples illustrating the theory.
