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Lectures on Algebraic Geometry I

2008-08-01 Mathematics
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Release : 2008-08-01
Genre : Mathematics
Kind : eBook
Book Rating : 016/5 ( reviews)

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Book Synopsis Lectures on Algebraic Geometry I by : Günter Harder

Download or read book Lectures on Algebraic Geometry I written by Günter Harder. This book was released on 2008-08-01. Available in PDF, EPUB and Kindle. Book excerpt: This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own. In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern methods have been anticipated by them.

Algebraic Geometry

2010-08-09 Mathematics
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Release : 2010-08-09
Genre : Mathematics
Kind : eBook
Book Rating : 221/5 ( reviews)

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Book Synopsis Algebraic Geometry by : Ulrich Görtz

Download or read book Algebraic Geometry written by Ulrich Görtz. This book was released on 2010-08-09. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. A systematic treatment and motivation of the theory is emphasized, using concrete examples to illustrate its usefulness. Several examples from the realm of Hilbert modular surfaces and of determinantal varieties are used methodically to discuss the covered techniques. Thus the reader experiences that the further development of the theory yields an ever better understanding of these fascinating objects. The text is complemented by many exercises that serve to check the comprehension of the text, treat further examples, or give an outlook on further results. The volume at hand is an introduction to schemes. To get startet, it requires only basic knowledge in abstract algebra and topology. Essential facts from commutative algebra are assembled in an appendix. It will be complemented by a second volume on the cohomology of schemes.

Lectures on Algebraic Geometry II

2011-04-21 Mathematics
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Release : 2011-04-21
Genre : Mathematics
Kind : eBook
Book Rating : 597/5 ( reviews)

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Book Synopsis Lectures on Algebraic Geometry II by : Günter Harder

Download or read book Lectures on Algebraic Geometry II written by Günter Harder. This book was released on 2011-04-21. Available in PDF, EPUB and Kindle. Book excerpt: This second volume introduces the concept of shemes, reviews some commutative algebra and introduces projective schemes. The finiteness theorem for coherent sheaves is proved, here again the techniques of homological algebra and sheaf cohomology are needed. In the last two chapters, projective curves over an arbitrary ground field are discussed, the theory of Jacobians is developed, and the existence of the Picard scheme is proved. Finally, the author gives some outlook into further developments- for instance étale cohomology- and states some fundamental theorems.

Lectures on Logarithmic Algebraic Geometry

2018-11-08 Mathematics
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Release : 2018-11-08
Genre : Mathematics
Kind : eBook
Book Rating : 737/5 ( reviews)

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Book Synopsis Lectures on Logarithmic Algebraic Geometry by : Arthur Ogus

Download or read book Lectures on Logarithmic Algebraic Geometry written by Arthur Ogus. This book was released on 2018-11-08. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to logarithmic geometry, a key tool for analyzing compactification and degeneration in algebraic geometry.

Lectures on Algebra

2006 Mathematics
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Release : 2006
Genre : Mathematics
Kind : eBook
Book Rating : 263/5 ( reviews)

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Book Synopsis Lectures on Algebra by : Shreeram Shankar Abhyankar

Download or read book Lectures on Algebra written by Shreeram Shankar Abhyankar. This book was released on 2006. Available in PDF, EPUB and Kindle. Book excerpt: This book is a timely survey of much of the algebra developed during the last several centuries including its applications to algebraic geometry and its potential use in geometric modeling. The present volume makes an ideal textbook for an abstract algebra course, while the forthcoming sequel. Lectures on Algebra II, will serve as a textbook for a linear algebra course. The author's fondness for algebraic geometry shows up in both volumes, and his recent preoccupation with the applications of group theory to the calculation of Galois groups is evident in the second volume which contains more local rings and more algebraic geometry. Both books are based on the author's lectures at Purdue University over the last few years.

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