MasayoshiMiyanishi
Affine Algebraic Geometry: Geometry Of Polynomial Rings
Affine Algebraic Geometry: Geometry Of Polynomial Rings
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- More about Affine Algebraic Geometry: Geometry Of Polynomial Rings
Algebraic geometry is more advanced with the completeness condition for projective or complete varieties, while non-complete varieties like affine algebraic varieties require sheaf cohomology. The Abhyankar-Moh-Suzuki Theorem and logarithmic geometry have made progress, covering vast basic material on a rigorous level.
Format: Hardback
Length: 440 pages
Publication date: 06 January 2024
Publisher: World Scientific Publishing Co Pte Ltd
Algebraic geometry, a branch of mathematics, delves into the study of algebraic structures and their geometric properties. It is particularly advanced when it comes to dealing with projective or complete varieties, which possess a completeness condition. These varieties are characterized by their finiteness or the vanishing of sheaf cohomologies, which provide valuable insights into their geometric characteristics.
However, for non-complete varieties like affine algebraic varieties, sheaf cohomology may not work as effectively. Research in this area used to be relatively slow, as affine spaces and polynomial rings, which form the fundamental building blocks of algebraic geometry, were challenging to understand.
Fortunately, significant progress has been made since the Abhyankar-Moh-Suzuki Theorem of embedded affine line was proved. This theorem opened up new avenues for research and led to the introduction of logarithmic geometry by Iitaka and Kawamata. The book, written by renowned experts in the field, covers a vast range of basic material on an extremely rigorous level. It provides a comprehensive introduction to algebraic geometry, covering topics such as affine varieties, projective varieties, sheaf cohomology, and logarithmic geometry.
For students and researchers interested in delving deeper into the world of algebraic geometry, this book is an invaluable resource. It offers a comprehensive and up-to-date account of the field, making it an essential tool for anyone seeking to advance their knowledge in this area.
ISBN-13: 9789811280085
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