Claudio Pedrini

Ciro Ciliberto

Fabrizio Catanese

Mauro C. Beltrametti

Antonio Lanteri

The volume consists of invited refereed research papers. The contributions cover a wide spectrum in algebraic geometry, from motives theory to numerical algebraic geometry and are mainly focused on higher dimensional varieties and Minimal Model Program and surfaces of general type. A part of the articles grew out a Conference in memory of Paolo Francia (1951-2000) held in Genova in September 2001 with about 70 participants.

A Volume in Memory of Paolo Francia

Algebraic Geometry

James McKernan

Ivan Cheltsov

Hubert Flenner

Yuri G. Prokhorov

Mikhail Zaidenberg

The main focus of this volume is on the problem of describing the automorphism groups of affine and projective varieties, a classical subject in algebraic geometry where, in both cases, the automorphism group is often infinite dimensional. The collection covers a wide range of topics and is intended for researchers in the fields of classical algebraic geometry and birational geometry (Cremona groups) as well as affine geometry with an emphasis on algebraic group actions and automorphism groups. It presents original research and surveys and provides a valuable overview of the current state of the art in these topics. Bringing together specialists from projective, birational algebraic geometry and affine and complex algebraic geometry, including Mori theory and algebraic group actions, this book is the result of ensuing talks and discussions from the conference “Groups of Automorphisms in Birational and Affine Geometry” held in October 2012, at the CIRM, Levico Terme, Italy. The talks at the conference highlighted the close connections between the above-mentioned areas and promoted the exchange of knowledge and methods from adjacent fields.

Levico Terme, Italy, October 2012

Automorphisms in Birational and Affine Geometry

Paulo Ribenboim

Edoardo Sernesi

Ruggiero Torelli

Collected papers of Ruggiero Torelli

M. Welleda Baldoni

G.M. Piacentini Cattaneo

In this volume one finds basic techniques from algebra and number theory (e.g. congruences, unique factorization domains, finite fields, quadratic residues, primality tests, continued fractions, etc.) which in recent years have proven to be extremely useful for applications to cryptography and coding theory. Both cryptography and codes have crucial applications in our daily lives, and they are described here, while the complexity problems that arise in implementing the related numerical algorithms are also taken into due account. Cryptography has been developed in great detail, both in its classical and more recent aspects. In particular public key cryptography is extensively discussed, the use of algebraic geometry, specifically of elliptic curves over finite fields, is illustrated, and a final chapter is devoted to quantum cryptography, which is the new frontier of the field. Coding theory is not discussed in full; however a chapter, sufficient for a good introduction to the subject, has been devoted to linear codes. Each chapter ends with several complements and with an extensive list of exercises, the solutions to most of which are included in the last chapter. Though the book contains advanced material, such as cryptography on elliptic curves, Goppa codes using algebraic curves over finite fields, and the recent AKS polynomial primality test, the authors' objective has been to keep the exposition as self-contained and elementary as possible. Therefore the book will be useful to students and researchers, both in theoretical (e.g. mathematicians) and in applied sciences (e.g. physicists, engineers, computer scientists, etc.) seeking a friendly introduction to the important subjects treated here. The book will also be useful for teachers who intend to give courses on these topics.

Elementary Number Theory, Cryptography and Codes

Giuseppe Veronese

Contains refereed papers related to the lectures and talks given at a conference held in Siena (Italy) in June 2004. Some of these papers contain expository sections, which describe the subject of special projective varieties and their applications. This book focusses on the topic of secant varieties and the classification of defective varieties.

A Volume in Memory of Giuseppe Veronese : Proceedings of the International Conference "Varieties with Unexpected Properties," Siena, Italy, June 8-13, 2004

Projective Varieties with Unexpected Properties

Ciro Ciliberto

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