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6.9 MB
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5014100768FA3A3F8316C11FE5DF1FF3C39C323D
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July 14, 2025, 12:38 p.m.
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(Last updated: July 14, 2025, 12:39 p.m.)
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| ['Clader E., Ross D. Beginning in Algebraic Geometry 2025.pdf'] | 0 bytes |
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2024-04-28
| Uploaded by indexFroggy | Size 890.7 KB | Health [ 3 /0 ] | Added 2024-04-28 |
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SOURCE: Clader E., Ross D. Beginning in Algebraic Geometry 2025
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MEDIAINFO
Textbook in PDF format Algebraic geometry, broadly defined as the geometric study of polynomial equations, is a subject that has now permeated nearly all of modern mathematics. After the subject was revolutionized in the second half of the twentieth century, in large part due to the work of Alexander Grothendieck, algebraic geometry began to develop a reputation for being an almost mythically powerful machine that was impenetrable to all but the initiated. Many beautiful texts were written to chip away at this barrier to entry, helping to make the geometric intuition behind algebraic geometry’s abstractions visible to students with only some grounding in commutative algebra and topology. There remains a population of learners to whom the gates of this subject are not yet fully open, though: those for whom the concepts of abstract algebra are a new language, one that has been encountered but not yet entirely internalized. While some may insist that comfort with such notions as quotient rings, modules, and algebras is a prerequisite to learning algebraic geometry, it is our belief that these ideas can be reinforced—in some cases even introduced—by seeing their manifestation in the geometric context. In addition to affording more students entry into algebraic geometry, this perspective has the advantage of allowing the algebra learner to restrict attention from the vast world of arbitrary rings to the more focused setting of polynomial rings, in which many notions are better-behaved and more intuitively motivated. It is largely for these learners that we wrote this book. Our intended audience has taken a first course in abstract algebra, so words such as “ring” and “ideal” are meaningful. However, our intended audience is also human, so having been exposed, for example, to the definition of a quotient ring does not necessarily mean that moving between viewing it as a collection of cosets and as an operation of “setting to zero” is entirely fluid. We strive to build facility in working with algebraic notions gradually and organically as it becomes relevant to the geometric narrative. On the other hand, we also anticipate that this book will be valuable to students with a more robust algebraic foundation who are eager to learn the foundations of algebraic geometry. While many of the algebraic ideas introduced in this book may not be new for such a student, we expect that revisiting and reinforcing those ideas in the geometric context will be a worthwhile endeavor
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