Ciro Ciliberto's Books

Elementary Number Theory, Cryptography and Codes

By: M. Welleda Baldoni,Ciro Ciliberto,G.M. Piacentini Cattaneo

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Elementary Number Theory, Cryptography and Codes

By: M. Welleda Baldoni,Ciro Ciliberto,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.

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530

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Springer Science & Business Media

Published Date

ISBN 10

3540692002

ISBN 13

9783540692003

Classification of Algebraic Varieties

Algebraic Geometry Conference on Classification of Algebraic Varieties, May 22-30, 1992, University of L'Aquila, L'Aquila, Italy

By: Ciro Ciliberto

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Classification of Algebraic Varieties

Algebraic Geometry Conference on Classification of Algebraic Varieties, May 22-30, 1992, University of L'Aquila, L'Aquila, Italy

By: Ciro Ciliberto

This volume contains the proceedings of the Algebraic Geometry Conference on Classification of Algebraic Varieties, held in May 1992 at the University of L'Aquila in Italy. The papers discuss a wide variety of problems that illustrate interactions between algebraic geometry and other branches of mathematics. Among the topics covered are algebraic curve theory, algebraic surface theory, the theory of minimal models, braid groups and the topology of algebraic varieties, toric varieties. In addition to algebraic geometers, theoretical physicists in some areas will find this book useful. The book is also suitable for an advanced graduate course in algebraic geometry, as it provides an overview of areas of current research.

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434

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821851799

ISBN 13

9780821851791

An Undergraduate Primer in Algebraic Geometry

By: Ciro Ciliberto

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An Undergraduate Primer in Algebraic Geometry

By: Ciro Ciliberto

This book consists of two parts. The first is devoted to an introduction to basic concepts in algebraic geometry: affine and projective varieties, some of their main attributes and examples. The second part is devoted to the theory of curves: local properties, affine and projective plane curves, resolution of singularities, linear equivalence of divisors and linear series, Riemann–Roch and Riemann–Hurwitz Theorems. The approach in this book is purely algebraic. The main tool is commutative algebra, from which the needed results are recalled, in most cases with proofs. The prerequisites consist of the knowledge of basics in affine and projective geometry, basic algebraic concepts regarding rings, modules, fields, linear algebra, basic notions in the theory of categories, and some elementary point–set topology. This book can be used as a textbook for an undergraduate course in algebraic geometry. The users of the book are not necessarily intended to become algebraic geometers but may be interested students or researchers who want to have a first smattering in the topic. The book contains several exercises, in which there are more examples and parts of the theory that are not fully developed in the text. Of some exercises, there are solutions at the end of each chapter.

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Page Count

327

Publisher

Springer Nature

Published Date

ISBN 10

3030710211

ISBN 13

9783030710217

An Undergraduate Primer in Algebraic Geometry

By: Ciro Ciliberto

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An Undergraduate Primer in Algebraic Geometry

By: Ciro Ciliberto

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327

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Springer Nature

Published Date

ISBN 10

3030710211

ISBN 13

9783030710217

Classification of Algebraic Varieties

Algebraic Geometry Conference on Classification of Algebraic Varieties, May 22-30, 1992, University of L'Aquila, L'Aquila, Italy

By: Ciro Ciliberto

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Classification of Algebraic Varieties

Algebraic Geometry Conference on Classification of Algebraic Varieties, May 22-30, 1992, University of L'Aquila, L'Aquila, Italy

By: Ciro Ciliberto

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434

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821851799

ISBN 13

9780821851791

Projective Varieties with Unexpected Properties

By: Ciro Ciliberto,Antony V. Geramita,Brian Harbourne,Kristian Ranestad

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Projective Varieties with Unexpected Properties

By: Ciro Ciliberto,Antony V. Geramita,Brian Harbourne,Kristian Ranestad

This volume contains refereed papers related to the lectures and talks given at a conference held in Siena (Italy) in June 2004. Also included are research papers that grew out of discussions among the participants and their collaborators. All the papers are research papers, but some of them also contain expository sections which aim to update the state of the art on the classical subject of special projective varieties and their applications and new trends like phylogenetic algebraic geometry. The topic of secant varieties and the classification of defective varieties is central and ubiquitous in this volume. Besides the intrinsic interest of the subject, it turns out that it is also relevant in other fields of mathematics like expressions of polynomials as sums of powers, polynomial interpolation, rank tensor computations, Bayesian networks, algebraic statistics and number theory.

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392

Published Date

ISBN 10

3119164259

ISBN 13

9783119164252

Elementary Number Theory, Cryptography and Codes

By: M. Welleda Baldoni,Ciro Ciliberto,G.M. Piacentini Cattaneo

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Elementary Number Theory, Cryptography and Codes

By: M. Welleda Baldoni,Ciro Ciliberto,G.M. Piacentini Cattaneo

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Write a review

Solve jigsaw puzzle

Age

Page Count

530

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540692002

ISBN 13

9783540692003

Book's by Ciro Ciliberto

Elementary Number Theory, Cryptography and Codes

Elementary Number Theory, Cryptography and Codes

Classification of Algebraic Varieties

Classification of Algebraic Varieties

An Undergraduate Primer in Algebraic Geometry

An Undergraduate Primer in Algebraic Geometry

An Undergraduate Primer in Algebraic Geometry

An Undergraduate Primer in Algebraic Geometry

Classification of Algebraic Varieties

Classification of Algebraic Varieties

Projective Varieties with Unexpected Properties

Projective Varieties with Unexpected Properties

Elementary Number Theory, Cryptography and Codes

Elementary Number Theory, Cryptography and Codes

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