Vector Bundles and Low Codimensional Subvarieties
Author: Gianfranco Casnati
Publisher:
Published: 2007
Total Pages: 412
ISBN-13:
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Vector Bundles in Algebraic Geometry
Author: Nigel J. Hitchin
Publisher:
Published: 1995
Total Pages: 345
ISBN-13: 9781139885195
DOWNLOAD EBOOKThe study of vector bundles over algebraic varieties has been stimulated over the last few years by successive waves of migrant concepts, largely from mathematical physics, whilst retaining its roots in old questions concerning subvarieties of projective space. The 1993 Durham Symposium on Vector Bundles in Algebraic Geometry brought together some of the leading researchers in the field to explore further these interactions. This book is a collection of survey articles by the main speakers at the symposium and presents to the mathematical world an overview of the key areas of research involving vector bundles. Topics covered include those linking gauge theory and geometric invariant theory such as augmented bundles and coherent systems; Donaldson invariants of algebraic surfaces; Floer homology and quantum cohomology; conformal field theory and the moduli spaces of bundles on curves; the Horrocks-Mumford bundle and codimension 2 subvarieties in P4 and P5; exceptional bundles and stable sheaves on projective space.
Classical Algebraic Geometry
Author: Igor V. Dolgachev
Publisher: Cambridge University Press
Published: 2012-08-16
Total Pages: 653
ISBN-13: 1107017653
DOWNLOAD EBOOKThis detailed exposition makes classical algebraic geometry accessible to the modern mathematician.
Connections Between Algebra, Combinatorics, and Geometry
Author: Susan M. Cooper
Publisher: Springer
Published: 2014-05-16
Total Pages: 328
ISBN-13: 1493906267
DOWNLOAD EBOOKCommutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2–3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resource for graduate students and researchers who wish to expand their knowledge of commutative algebra, algebraic geometry, combinatorics, and the intricacies of their intersection.
Commutative Algebra
Author: Irena Peeva
Publisher: Springer Science & Business Media
Published: 2013-02-01
Total Pages: 705
ISBN-13: 1461452929
DOWNLOAD EBOOKThis contributed volume brings together the highest quality expository papers written by leaders and talented junior mathematicians in the field of Commutative Algebra. Contributions cover a very wide range of topics, including core areas in Commutative Algebra and also relations to Algebraic Geometry, Algebraic Combinatorics, Hyperplane Arrangements, Homological Algebra, and String Theory. The book aims to showcase the area, especially for the benefit of junior mathematicians and researchers who are new to the field; it will aid them in broadening their background and to gain a deeper understanding of the current research in this area. Exciting developments are surveyed and many open problems are discussed with the aspiration to inspire the readers and foster further research.
Vector Bundles in Algebraic Geometry
Author: N. J. Hitchin
Publisher: Cambridge University Press
Published: 1995-03-16
Total Pages: 359
ISBN-13: 0521498783
DOWNLOAD EBOOKThis book is a collection of survey articles by the main speakers at the 1993 Durham symposium on vector bundles in algebraic geometry.
Geometry and Complexity Theory
Author: J. M. Landsberg
Publisher: Cambridge University Press
Published: 2017-09-28
Total Pages: 353
ISBN-13: 110819141X
DOWNLOAD EBOOKTwo central problems in computer science are P vs NP and the complexity of matrix multiplication. The first is also a leading candidate for the greatest unsolved problem in mathematics. The second is of enormous practical and theoretical importance. Algebraic geometry and representation theory provide fertile ground for advancing work on these problems and others in complexity. This introduction to algebraic complexity theory for graduate students and researchers in computer science and mathematics features concrete examples that demonstrate the application of geometric techniques to real world problems. Written by a noted expert in the field, it offers numerous open questions to motivate future research. Complexity theory has rejuvenated classical geometric questions and brought different areas of mathematics together in new ways. This book will show the beautiful, interesting, and important questions that have arisen as a result.
Constructing Vector Bundles from Codimension-two Subvarieties
Author: Johannes Albert Vogelaar
Publisher:
Published: 1978
Total Pages: 54
ISBN-13:
DOWNLOAD EBOOKPositivity in Algebraic Geometry II
Author: R.K. Lazarsfeld
Publisher: Springer
Published: 2017-07-25
Total Pages: 392
ISBN-13: 3642188109
DOWNLOAD EBOOKTwo volume work containing a contemporary account on "Positivity in Algebraic Geometry". Both volumes also available as hardcover editions as Vols. 48 and 49 in the series "Ergebnisse der Mathematik und ihrer Grenzgebiete". A good deal of the material has not previously appeared in book form. Volume II is more at the research level and somewhat more specialized than Volume I. Volume II contains a survey of positivity for vector bundles, and moves on to a systematic development of the theory of multiplier ideals and their applications. Contains many concrete examples, applications, and pointers to further developments
Vector Bundles and Their Applications
Author: Glenys Luke
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 259
ISBN-13: 1475769237
DOWNLOAD EBOOKThe book is devoted to the basic notions of vector bundles and their applications. The focus of attention is towards explaining the most important notions and geometric constructions connected with the theory of vector bundles. Theorems are not always formulated in maximal generality but rather in such a way that the geometric nature of the objects comes to the fore. Whenever possible examples are given to illustrate the role of vector bundles. Audience: With numerous illustrations and applications to various problems in mathematics and the sciences, the book will be of interest to a range of graduate students from pure and applied mathematics.
