Affine Space Fibrations (Studies in Mathematics)

Hardcover, xi + 346 pages, NOT ex-library. Limited gentle handling wear, book is clean and bright with unmarked text, free of inscriptions and stamps, firmly bound. Issued without a dust jacket. -- This research monograph confronts a fundamental and surprisingly difficult question in algebraic geometry: if you have a geometric object (an affine variety) that is formed by stacking affine spaces (like lines or planes), what can you say about its structure? This question is central to famous unsolved problems like the Zariski Cancellation Problem. The analysis provides a comprehensive toolbox for tackling these questions, with a deep focus on developing and using special algebraic "invariants" - properties that remain unchanged even when the variety is transformed. These tools, such as the Makar-Limanov and Derksen invariants, are then rigorously applied to distinguish between geometric objects that look superficially similar but are fundamentally different, with special attention paid to key counterexamples like Danielewski surfaces. The work serves as a self-contained guide, consolidating decades of advanced research into a coherent and systematic exposition.…