Affine Algebraic Geometry: Geometry of Polynomial Rings
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Affine Algebraic Geometry: Geometry of Polynomial Rings

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Description

Affine Algebraic Geometry: Geometry of Polynomial RingsAlgebraic 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

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:

  • It begins with an introduction to algebraic geometry which comprises almost all results in commutative algebra and algebraic geometry.
  • Arguments frequently used in affine algebraic geometry are elucidated by treating affine lines embedded in the affine plane and automorphism theorem of the affine plane. There is also a detailed explanation on affine algebraic surfaces which resemble the affine plane in the ring-theoretic nature and for actions of algebraic groups.
  • The Jacobian conjecture for these surfaces is also considered by making use of the results and tools already presented in this book. The conjecture has been thought as one of the most unattackable problems even in dimension two.
  • Advanced results are collected in appendices of chapters so that readers can understand the main streams of arguments.
  • There are abundant problems in the first three chapters which come with hints and ideas for proof.

 

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SKU: 1699062286

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I needed to replace the wiper blades on my Jeep Wrangler JK, so I first went to a local auto parts store. The prices were pretty expensive, and they didn’t even have the correct replacement for my rear wiper blade. That’s when I decided to order the UTOBOO 15"+15" Windshield Wipers with 13 Inch Rear Wiper Blade Replacement online, and I’m really glad I did. The set arrived quickly and included everything I needed for both the front and rear wipers. Installation was very easy and only took a few minutes. They fit well on my Jeep, and the blades feel sturdy and made from good-quality materials. After using them, they wipe smoothly and leave the windshield clean without streaks, which is exactly what you want, especially in rain or dusty conditions. Overall, this is a great value compared to buying individual blades in-store, and it’s especially convenient since it includes the rear wiper replacement too. I would definitely recommend these to other Jeep Wrangler owners looking for an affordable and reliable option. ------Tip, don't forget to take off the green plastic, If you check the comments many people argues that the wipers don't work but in the pictures you can see they did not take off the green plastic protector. ----
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