Algebraic Geometry

Graduate Texts in Mathematics #52

by Robin Hartshorne

Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and will J.-P. Serre and A. Grothendieck in Paris. After receiving his Ph.D. from Princeton in 1963, Hartshrne became a Junior Fellow at Harvard, then taught there for several years. In 1972 he moved to California where he is now Professor at the University of California at Berkeley. He is the author of Residues and Duality(1966), Foundations of Projective Geometry (1967), Ample Subvarieties of Algebraic Varieties (1970), and numerous research articles. His current research interest is the geometry of projective varieties and vector bundles. He has been a visiting professor at the College de France and at Kyoto University, where he gave his lectures in French and in Japanese, respectively.

Professor Hartshrne is married to Edie Churchill, educator, musician and therapist, and has two sons and one daughter. He has travelled widely, speaks several foreign languages, and is an experienced mountain climber. He is also an accomplished musician, playing flute, piano, and traditional Japanese music on the shakuhachi.

Genres: Mathematics, Geometry, Algebra, Textbooks, Nonfiction, Number Theory

512 pages, Hardcover

First published December 19, 1977

Reviews

[jeremy wang · Rating 3 out of 5]

lmao i hate myself

[Davis · Rating 5 out of 5]

My PhD advisor inherited a pedagogical approach to Algebraic Geometry from his own advisor: to prepare them for research, have your advisees work through the entirety of this text, including all of the problems. It's an arduous, strenuous process -- the text is dense, and many of the problems are actually important theorems in AG (woe unto the reader who skips them!). Even though most of the material in this book is 30 years old, it's a relatively small step to go from completing Hartshorne to catching up with some cutting-edge research in the field (and thence to making novel contributions).

[Will · Rating 3 out of 5]

This book has a strange organization. The main text tantalizes you with a beautiful story, but it leaves out all the details and forces you to write out the details yourself. What kind of book makes you write your own story?

[Darren Tapp · Rating 5 out of 5]

This is a very good book for a second or third year math grad student interested in Algebraic Geometry. The subject is presented with the modern language of sheaves and schemes as developed by Serre and Grothendieck. This books contains relevant exercises that can help a student determine if he or she has really understood the material.

[Ghost · Rating 4 out of 5]

autor chyba nasladowal adama mickiewicza podczas pisania pana tadeusza bo to na pewno nie bylo pisane na trzezwo

[Daniel Apsley · Rating 5 out of 5]

Fyodor Dostoevsky supposedly said, "The degree of civilization in a society can be judged by entering its prisons." He would have judged well, I think.

[Carlo Mazzanti · Rating 5 out of 5]

My bible, as it should be anyone's.

[James Swenson · Rating 2 out of 5]

Where's the geometry? It would be far too easy to spend a year reading this book and end up knowing that the Krull dimension of the ring k[x,y] is two, but unable to explain why this indicates that "dimension" is a good name for the concept.

I was shocked to see that the author, in describing this book, uses a sentence that starts with the words, "And most important, we give lots of specific examples...." This struck me as a direct lie, until I read the rest of the sentence: "in the form of exercises at the end of each section."

This is a great reference, but I wouldn't use it for any other purpose.

[Sam Chow · Rating 4 out of 5]

The presentation is effective as long as you do all of the exercises in order; so it's a long road, but the exercises are at quite a nice difficulty level for a graduate student. The treatment is restricted to algebraically closed fields, so arithmetic geometers need something to supplement this. If the end goal is schemes or something even more general then this may be too indirect a route, but for vanilla algebraic geometry it seems like quite a good treatment. A first course in commutative algebra is recommended as background knowledge.

[Dan · Rating 2 out of 5]

This book is dense, which is good because it has lots of information in it. That said, it is probably not the best book to learn algebraic geometry from. Personally, I found it pretty difficult to learn algebraic geometry from this book.

However, I get the impression that if you already know algebraic geometry, this is an indispensable resource.

UPDATE: I also used this book to learn about Sheaf Cohomology. I actually found it quite helpful to learn about these subjects.

[Geoffrey Lee · Rating 2 out of 5]

I had great trouble with chapter two of this book. Some of my confusion has been mitigated after finding Eisenbud's book The Geometry of Schemes, but I am still trying to familiarize myself with the subject. Seriously though, prepare yourself for hours of banging your head on desks and flipping through pages to find definitions. I find it for some odd reason very hard to retain memory of what I read in this book making it necessary to read pages several times.