Polynomial Rings and Affine Algebraic Geometry

1. Front Matter

   Pages i-x

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2. On Fano Schemes of Complete Intersections

   • C. Ciliberto, M. Zaidenberg

   Pages 1-39

3. Locally Nilpotent Sets of Derivations

   • Daniel Daigle

   Pages 41-71

4. On the Theory of Gordan-Noether on Homogeneous Forms with Zero Hessian (Improved Version)

   • Junzo Watanabe, Michiel de Bondt

   Pages 73-107

5. Rational Real Algebraic Models of Compact Differential Surfaces with Circle Actions

   • Adrien Dubouloz, Charlie Petitjean

   Pages 109-142

6. The Super-Rank of a Locally Nilpotent Derivation of a Polynomial Ring

   • Gene Freudenburg

   Pages 143-150

7. Affine Space Fibrations

   • Rajendra V. Gurjar, Kayo Masuda, Masayoshi Miyanishi

   Pages 151-193

8. A Graded Domain Is Determined at Its Vertex. Applications to Invariant Theory

   • R. V. Gurjar

   Pages 195-198

9. Singularities of Normal Log Canonical del Pezzo Surfaces of Rank One

   • Hideo Kojima

   Pages 199-208

10. \(O_2(\mathbb {C})\)-Vector Bundles and Equivariant Real Circle Actions

    • L. Moser-Jauslin

    Pages 209-221

11. On Some Sufficient Conditions for Polynomials to Be Closed Polynomials over Domains

    • Takanori Nagamine

    Pages 223-231

12. Variations on the Theme of Zariski’s Cancellation Problem

    • Vladimir L. Popov

    Pages 233-250

13. Tango Structures on Curves in Characteristic 2

    • Yoshifumi Takeda

    Pages 251-265

14. Exponential Matrices of Size Five-By-Five

    • Ryuji Tanimoto

    Pages 267-305

15. Mathieu-Zhao Spaces and the Jacobian Conjecture

    • Arno van den Essen

    Pages 307-315

This proceedings volume gathers selected, peer-reviewed works presented at the Polynomial Rings and Affine Algebraic Geometry Conference, which was held at Tokyo Metropolitan University on February 12-16, 2018. Readers will find some of the latest research conducted by an international group of experts on affine and projective algebraic geometry. The topics covered include group actions and linearization, automorphism groups and their structure as infinite-dimensional varieties, invariant theory, the Cancellation Problem, the Embedding Problem, Mathieu spaces and the Jacobian Conjecture, the Dolgachev-Weisfeiler Conjecture, classification of curves and surfaces, real forms of complex varieties, and questions of rationality, unirationality, and birationality. These papers will be of interest to all researchers and graduate students working in the fields of affine and projective algebraic geometry, as well as on certain aspects of commutative algebra, Lie theory, symplectic geometry andStein manifolds.

• affine variety
• locally nilpotent derivation
• automorphism group
• projective variety
• rational curve
• Ga-action
• Mathieu space
• Jacobian Conjecture
• log Kodaira dimension

• Department of Mathematical Sciences, Tokyo Metropolitan University, Hachioji, Tokyo, Japan

  Shigeru Kuroda

• Faculty of Applied Physics, University of Fukui, Fukui, Japan

  Nobuharu Onoda

• Department of Mathematics, Western Michigan University, Kalamazoo, USA

  Gene Freudenburg

Shigeru Kuroda is a Professor at Tokyo Metropolitan University, Japan. Holding a PhD (2003) from Tohoku University, Japan, his main research focuses are on affine algebraic geometry and polynomial ring theory.


Nobuharu Onoda is a Professor at University of Fukui, Japan. He holds a PhD (1983) from Osaka University, Japan. His main research interests are in commutative algebra related to affine algebraic geometry.

Gene Freudenburg is a Professor at Western Michigan University, USA. He completed his PhD (1992) at Washington University, Saint Louis, USA. His chief research interests are in commutative algebra and affine algebraic geometry. He authored the Springer book “Algebraic Theory of Locally Nilpotent Derivations” (978-3-662-55348-0), now in its second edition.

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