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Current Developments in Algebraic Geometry
This volume, based on a workshop by the MSRI, offers an overview of the state of the art in many areas of algebraic geometry.
Algebraic Geometry
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.
Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
This book constitutes the strictly refereed proceedings of the 12th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-12, held in Toulouse, France, June 1997. The 27 revised full papers presented were carefully selected by the program committee for inclusion in the volume. The papers address a broad range of current issues in coding theory and computer algebra spanning polynomials, factorization, commutative algebra, real geometry, group theory, etc. on the mathematical side as well as software systems, telecommunication, complexity theory, compression, signal processing, etc. on the computer science and engineering side.
A First Course In Algebraic Geometry And Algebraic Varieties
This book provides a gentle introduction to the foundations of Algebraic Geometry, starting from computational topics (ideals and homogeneous ideals, zero loci of ideals) up to increasingly intrinsic and abstract arguments, such as 'Algebraic Varieties', whose natural continuation is a more advanced course on the theory of schemes, vector bundles, and sheaf-cohomology.Valuable to students studying Algebraic Geometry and Geometry, this title contains around 60 exercises (with solutions) to help students thoroughly understand the theories introduced in the book. Proofs of the results are carried out in full detail. Many examples are discussed in order to reinforce the understanding of both the theoretical elements and their consequences, as well as the possible applications of the material.
Local and Global Methods in Algebraic Geometry
This volume contains the proceedings of the conference Local and Global Methods in Algebraic Geometry, held from May 12–15, 2016, at the University of Illinois at Chicago, in honor of Lawrence Ein's 60th birthday. The articles cover a broad range of topics in algebraic geometry and related fields, including birational geometry and moduli theory, analytic and positive characteristic methods, geometry of surfaces, singularity theory, hyper-Kähler geometry, rational points, and rational curves.
From Classical to Modern Algebraic Geometry
This book commemorates the 150th birthday of Corrado Segre, one of the founders of the Italian School of Algebraic Geometry and a crucial figure in the history of Algebraic Geometry. It is the outcome of a conference held in Turin, Italy. One of the book's most unique features is the inclusion of a previously unpublished manuscript by Corrado Segre, together with a scientific commentary. Representing a prelude to Segre's seminal 1894 contribution on the theory of algebraic curves, this manuscript and other important archival sources included in the essays shed new light on the eminent role he played at the international level. Including both survey articles and original research papers, the book is divided into three parts: section one focuses on the implications of Segre's work in a historic light, while section two presents new results in his field, namely Algebraic Geometry. The third part features Segre's unpublished notebook: Sulla Geometria Sugli Enti Algebrici Semplicemente Infiniti (1890-1891). This volume will appeal to scholars in the History of Mathematics, as well as to researchers in the current subfields of Algebraic Geometry.
Surveys on Recent Developments in Algebraic Geometry
The algebraic geometry community has a tradition of running a summer research institute every ten years. During these influential meetings a large number of mathematicians from around the world convene to overview the developments of the past decade and to outline the most fundamental and far-reaching problems for the next. The meeting is preceded by a Bootcamp aimed at graduate students and young researchers. This volume collects ten surveys that grew out of the Bootcamp, held July 6–10, 2015, at University of Utah, Salt Lake City, Utah. These papers give succinct and thorough introductions to some of the most important and exciting developments in algebraic geometry in the last decade. Included are descriptions of the striking advances in the Minimal Model Program, moduli spaces, derived categories, Bridgeland stability, motivic homotopy theory, methods in characteristic and Hodge theory. Surveys contain many examples, exercises and open problems, which will make this volume an invaluable and enduring resource for researchers looking for new directions.
Compact Moduli Spaces and Vector Bundles
This book contains the proceedings of the conference on Compact Moduli and Vector Bundles, held from October 21-24, 2010, at the University of Georgia. This book is a mix of survey papers and original research articles on two related subjects: Compact Moduli spaces of algebraic varieties, including of higher-dimensional stable varieties and pairs, and Vector Bundles on such compact moduli spaces, including the conformal block bundles. These bundles originated in the 1970s in physics; the celebrated Verlinde formula computes their ranks. Among the surveys are those that examine compact moduli spaces of surfaces of general type and others that concern the GIT constructions of log canonical models of moduli of stable curves. The original research articles include, among others, papers on a formula for the Chern classes of conformal classes of conformal block bundles on the moduli spaces of stable curves, on Looijenga's conjectures, on algebraic and tropical Brill-Noether theory, on Green's conjecture, on rigid curves on moduli of curves, and on Steiner surfaces.
Classification of Irregular Varieties
M. Andreatta, E. Ballico, J. Wisniewski: Projective manifolds containing large linear subspaces; - F. Bardelli: Algebraic cohomology classes on some specialthreefolds; - Ch. Birkenhake, H. Lange: Norm-endomorphisms of abelian subvarieties; - C. Ciliberto, G.van der Geer: On the jacobian of ahyperplane section of a surface; - C. Ciliberto, H. Harris, M. Teixidor i Bigas: On the endomorphisms of Jac (W1d(C)) when p=1 and C has general moduli; - B. van Geemen: Projective models of Picard modular varieties; - J. Kollar, Y. Miyaoka, S. Mori: Rational curves on Fano varieties; - R. Salvati Manni: Modular forms of the fourth degree; A. Vistoli: Equivariant Grothendieck groups and equivariant Chow groups; - Trento examples; Open problems.
