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Description
Introduction to Algebraic GeometryAuthor Serge Lang defines algebraic geometry as the study of systems of algebraic equations in several variables and of the structure that one can give to the solutions of such equations. The study can be carried out in four ways: analytical, topological, algebraico geometric, and arithmetic. This volume offers a rapid, concise, and self contained introductory approach to the algebraic aspects of the third method, the algebraico geometric. The
Author Serge Lang defines algebraic geometry as the study of systems of algebraic equations in several variables and of the structure that one can give to the solutions of such equations. The study can be carried out in four ways: analytical, topological, algebraico-geometric, and arithmetic. This volume offers a rapid, concise, and self-contained introductory approach to the algebraic aspects of the third method, the algebraico-geometric. The treatment assumes only familiarity with elementary algebra up to the level of Galois theory.Starting with an opening chapter on the general theory of places, the author advances to examinations of algebraic varieties, the absolute theory of varieties, and products, projections, and correspondences. Subsequent chapters explore normal varieties, divisors and linear systems, differential forms, the theory of simple points, and algebraic groups, concluding with a focus on the Riemann-Roch theorem. All the theorems of a general nature related to the foundations of the theory of algebraic groups are featured.
Binding Type: Paperback
Publisher: Dover Publications
Published: 03/20/2019
ISBN: 9780486834221
Pages: 272
Weight: 0.85lbs
Size: 8.90h x 5.90w x 0.60d
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Product Reviews
★★★★★ 1
Not Tuff
Color: Black Yellow Phrog, Color: Black Yellow Phrog
Absolutely terrible and not “tuff” at all. My chocolate lab had this thing destroyed in less than two hours. I would not recommend these for the price.
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Reviewed in the United States on April 11, 2026
★★★★★ 3
Cute but Not Durable
Color: 2PK Green Leaping Phrog
⭐️⭐️⭐️⭐️ Cute but Not Durable
Super cute toy—my dogs loved it right away! Unfortunately, they chewed the head off within a few hours. I ordered a second one because they were so into it, but the same thing happened again.
I won’t be ordering a third, but they still play with their two headless frogs. So while it’s not the most durable, it definitely kept them entertained!
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Reviewed in the United States on June 9, 2025
★★★★★ 5
Great toy
Color: Black/Orange
This brand really makes durable toys. They outlast every other toy my dogs have. One dog loves to get the squeaker out of any toy, but he doesn’t rip this one apart. Obviously it won’t last forever, but no toy does! Some other brands of toys only make it a day or two, while these last months to years.
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Reviewed in the United States on May 10, 2026
★★★★★ 5
Super durable!
Color: 2PK Green Leaping Phrog
Yellow lab approved bc they are fun to chew. Mom approved because they last forever!
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Reviewed in the United States on January 7, 2026
★★★★★ 5
Great toy for two big German Shepherds
Color: Brown
We only buy Tuffy dog toys now because we have one German Shepherd, and we often watch our daughter's GSD too, and the two dogs tear anything else apart in minutes. Tuffy toys are BY FAR superior to any other dog toy we have tried.
That being said, some Tuffy toys seem to last longer than others with the two dogs, and this one has been pretty good! We've had it for a few weeks now, and it's just now starting to show some white (stuffing) where their teeth have pierced the top of the toy.
That's pretty good, considering they play tug of war with it and can tear into toys pretty hard. If it were just our one dog, I think it would last a lot longer because it's the tug of war between the two of them that does them in faster.
Even so, when they do manage to tear the fabric in vulnerable places, I just pull the stuffing out from that area, and they continue to play with it, sometimes for months!
This one is better than some other Tuffy toys too because it has lots of areas where there is already more fabric and reinforced seams than stuffing, like all the legs on the side, the tail, and even the pincers. So far, they haven't been able to tear into those at all. Just a bit on the top of the head, and so far, no stuffing coming out yet.
This one is a big win for us! When they finally do do it in, I will turn around and buy another Scorch the Scorpion right away!
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Reviewed in the United States on May 5, 2014