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Ciliberto, C. and Zaidenberg, M: On Fano schemes of complete intersections.- Daigle, D.: Locally nilpotent sets of derivations.- DeBondt, M. and Watanabe, J: On the theory of Gordan-Noether on homogeneous forms with zero Hessian.- Dubouloz, A. and Petitijean, C: Rational real algebraic models of compact differential surfaces with circle actions.- Freudenburg, G.: The super-rank of a locally nilpotent derivation of a polynomial ring.- Gurjar, R., Masuda, K., and Miyanishi, M: Affine space fibrations.- Gurjar, R.: A graded domain is determined at its vertex: Applications to invariant theory.- Kojima, H.: Singularities of normal log canonical del Pezzo surfaces of rank one.- Moser-Jauslin, L.: O2(C)-vector bundles and equivariant real circle actions.- Nagamine, T.: On some sufficient conditions for polynomials to be closed polynomials over Domains.- Popov, V.: Variations on the theme of Zariski’s Cancellation Problem.- Takeda, Y.: Tango structures on curves in characteristic 2.- Tanimoto, R.: Exponential matrices of size five-by-five.- Van den Essen, A.: Mathieu-Zhao Spaces and the Jacobian Conjecture.<p></p><p></p><br>

<div><b>Shigeru Kuroda</b> 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.</div><div><b><br></b></div><div><b>Nobuharu Onoda</b> 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.<br></div><div><p></p></div><div><br></div><div><b>Gene Freudenburg</b> 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.</div><div><br></div>

This proceedings volume gathers together selected, peer-reviewed works presented at the Polynomial Rings and Affine Algebraic Geometry conference which was held at the Tokyo Metropolitan University on February 12-26, 2018, in Tokyo, Japan. In this book, the reader will find some of the latest research conducted by an international group of experts in affine and projective algebraic geometry. 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. The articles contained in this volume will be of interest to all researchers and graduate students working in the fields of affine and projective algebraic geometry, as well as in certain aspects of commutative algebra, Lie theory, symplectic geometry and Stein manifolds.<br>

Gathers in a single volume the latest research conducted by an international group of experts on affine and projective algebraic geometry Covers topics like the Cancellation Problem, the Embedding Problem, the Dolgachev-Weisfeiler Conjecture, and more Offers a valuable source of information and inspiration for researchers and students pursuing new problems and research paths