Affine Algebraic Geometry: Geometry Of Polynomial Rings

Download or read book Affine Algebraic Geometry: Geometry Of Polynomial Rings written by Masayoshi Miyanishi and published by World Scientific. This book was released on 2023-12-05 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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: