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Lectures on Algebraic Geometry II

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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 Algebraic Geometry I

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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 II

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Release : 2015
Genre : Algebraic varieties
Kind : eBook
Book Rating : 809/5 ( reviews)

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Book Synopsis Algebraic Geometry II by : David Mumford

Download or read book Algebraic Geometry II written by David Mumford. This book was released on 2015. Available in PDF, EPUB and Kindle. Book excerpt: Several generations of students of algebraic geometry have learned the subject from David Mumford's fabled "Red Book" containing notes of his lectures at Harvard University. This book contains what Mumford had intended to be Volume II. It covers the material in the "Red Book" in more depth with several more topics added.

Lectures on Logarithmic Algebraic Geometry

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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.

Algebraic Geometry

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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.

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