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This Lecture Notes is meant to introduce noncommutative algebraic geometry tools (which were invented by M. Artin, W. Schelter, J. Tate, and M. Van den Bergh in the late 1980s) and also graded skew Clifford algebras (which were introduced by T. Cassidy and M. Vancliff).

These are lecture notes from the IMPANGA 2010 Summer School. The lectures survey some of the main features of equivariant cohomology at an introductory level. The first part is an overview, including basic definitions and examples. In the second lecture, I discuss one of the most useful aspects of the theory: the possibility of localizing at fixed points without losing information. The third lecture focuses on Grassmannians, and describes some recent positivity results about their equivariant cohomology rings.

These are lecture notes from the IMPANGA 2010 Summer School. The lectures survey some of the main features of equivariant cohomology at an introductory level. The first part is an overview, including basic definitions and examples. In the second lecture, I discuss one of the most useful aspects of the theory: the possibility of localizing at fixed points without losing information. The third lecture focuses on Grassmannians, and describes some recent positivity results about their equivariant cohomology rings.

These are lecture notes from the IMPANGA 2010 Summer School. The lectures survey some of the main features of equivariant cohomology at an introductory level. The first part is an overview, including basic definitions and examples. In the second lecture, I discuss one of the most useful aspects of the theory: the possibility of localizing at fixed points without losing information. The third lecture focuses on Grassmannians, and describes some recent positivity results about their equivariant cohomology rings.

XIII, 538 p

XIII, 538 p

We present an introduction to the theory of algebraic geometry codes. Starting from evaluation codes and codes from order and weight functions, special attention is given to one-point codes and, in particular, to the family of Castle codes.

These notes assemble the contents of the introductory courses I have been giving at SISSA since 1995/96. Originally the course was intended as introduction to (complex) algebraic geometry for students with an education in theoretical physics, to help them to master the basic algebraic geometric tools necessary for doing research in algebraically integrable systems and in the geometry of quantum eld theory and string theory. This motivation still transpires from the chapters in the second part of these notes. The rst part on the contrary is a brief but rather systematic introduction to two topics, singular homology (Chapter 2) and sheaf theory, including their cohomology (Chapter 3). Chapter 1 assembles some basics fact in homological algebra and develops the rst rudiments of de Rham cohomology, with the aim of providing an example to the various abstract constructions. Chapter 5 is an introduction to spectral sequences, a rather intricate but very powerful computation tool. The examples provided here are from sheaf theory but this computational techniques is also very useful in algebraic topology. Lecture Notes Collection FreeScience.info ID2390 Obtained from http://people.sissa.it/~bruzzo/notes/IATG/notes.pdf http://www.freescience.info/go.php?pagename=books&id=2390

These notes assemble the contents of the introductory courses I have been giving at SISSA since 1995/96. Originally the course was intended as introduction to (complex) algebraic geometry for students with an education in theoretical physics, to help them to master the basic algebraic geometric tools necessary for doing research in algebraically integrable systems and in the geometry of quantum eld theory and string theory. This motivation still transpires from the chapters in the second part of these notes. The rst part on the contrary is a brief but rather systematic introduction to two topics, singular homology (Chapter 2) and sheaf theory, including their cohomology (Chapter 3). Chapter 1 assembles some basics fact in homological algebra and develops the rst rudiments of de Rham cohomology, with the aim of providing an example to the various abstract constructions. Chapter 5 is an introduction to spectral sequences, a rather intricate but very powerful computation tool. The examples provided here are from sheaf theory but this computational techniques is also very useful in algebraic topology. Lecture Notes Collection FreeScience.info ID2390 Obtained from http://people.sissa.it/~bruzzo/notes/IATG/notes.pdf http://www.freescience.info/go.php?pagename=books&id=2390

These notes assemble the contents of the introductory courses I have been giving at SISSA since 1995/96. Originally the course was intended as introduction to (complex) algebraic geometry for students with an education in theoretical physics, to help them to master the basic algebraic geometric tools necessary for doing research in algebraically integrable systems and in the geometry of quantum eld theory and string theory. This motivation still transpires from the chapters in the second part of these notes. The rst part on the contrary is a brief but rather systematic introduction to two topics, singular homology (Chapter 2) and sheaf theory, including their cohomology (Chapter 3). Chapter 1 assembles some basics fact in homological algebra and develops the rst rudiments of de Rham cohomology, with the aim of providing an example to the various abstract constructions. Chapter 5 is an introduction to spectral sequences, a rather intricate but very powerful computation tool. The examples provided here are from sheaf theory but this computational techniques is also very useful in algebraic topology. Lecture Notes Collection FreeScience.info ID2390 Obtained from http://people.sissa.it/~bruzzo/notes/IATG/notes.pdf http://www.freescience.info/go.php?pagename=books&id=2390

These notes assemble the contents of the introductory courses I have been giving at SISSA since 1995/96. Originally the course was intended as introduction to (complex) algebraic geometry for students with an education in theoretical physics, to help them to master the basic algebraic geometric tools necessary for doing research in algebraically integrable systems and in the geometry of quantum eld theory and string theory. This motivation still transpires from the chapters in the second part of these notes. The rst part on the contrary is a brief but rather systematic introduction to two topics, singular homology (Chapter 2) and sheaf theory, including their cohomology (Chapter 3). Chapter 1 assembles some basics fact in homological algebra and develops the rst rudiments of de Rham cohomology, with the aim of providing an example to the various abstract constructions. Chapter 5 is an introduction to spectral sequences, a rather intricate but very powerful computation tool. The examples provided here are from sheaf theory but this computational techniques is also very useful in algebraic topology. Lecture Notes Collection FreeScience.info ID2390 Obtained from http://people.sissa.it/~bruzzo/notes/IATG/notes.pdf http://www.freescience.info/go.php?pagename=books&id=2390

These notes assemble the contents of the introductory courses I have been giving at SISSA since 1995/96. Originally the course was intended as introduction to (complex) algebraic geometry for students with an education in theoretical physics, to help them to master the basic algebraic geometric tools necessary for doing research in algebraically integrable systems and in the geometry of quantum eld theory and string theory. This motivation still transpires from the chapters in the second part of these notes. The rst part on the contrary is a brief but rather systematic introduction to two topics, singular homology (Chapter 2) and sheaf theory, including their cohomology (Chapter 3). Chapter 1 assembles some basics fact in homological algebra and develops the rst rudiments of de Rham cohomology, with the aim of providing an example to the various abstract constructions. Chapter 5 is an introduction to spectral sequences, a rather intricate but very powerful computation tool. The examples provided here are from sheaf theory but this computational techniques is also very useful in algebraic topology. Lecture Notes Collection FreeScience.info ID2390 Obtained from http://people.sissa.it/~bruzzo/notes/IATG/notes.pdf http://www.freescience.info/go.php?pagename=books&id=2390

These notes assemble the contents of the introductory courses I have been giving at SISSA since 1995/96. Originally the course was intended as introduction to (complex) algebraic geometry for students with an education in theoretical physics, to help them to master the basic algebraic geometric tools necessary for doing research in algebraically integrable systems and in the geometry of quantum eld theory and string theory. This motivation still transpires from the chapters in the second part of these notes. The rst part on the contrary is a brief but rather systematic introduction to two topics, singular homology (Chapter 2) and sheaf theory, including their cohomology (Chapter 3). Chapter 1 assembles some basics fact in homological algebra and develops the rst rudiments of de Rham cohomology, with the aim of providing an example to the various abstract constructions. Chapter 5 is an introduction to spectral sequences, a rather intricate but very powerful computation tool. The examples provided here are from sheaf theory but this computational techniques is also very useful in algebraic topology. Lecture Notes Collection FreeScience.info ID2390 Obtained from http://people.sissa.it/~bruzzo/notes/IATG/notes.pdf http://www.freescience.info/go.php?pagename=books&id=2390

Introduction to Algebraic Geometry

This is an expository introduction to tropical algebraic geometry based on my lectures at the Workshop on Tropical Geometry and Integrable Systems in Glasgow, July 4-8, 2011, and at the ELGA 2011 school on Algebraic Geometry and Applications in Buenos Aires, August 1-5, 2011.

This is a survey of the author's paper arXiv:1001.0023 on "Algebraic Geometry over C-infinity rings". If X is a smooth manifold then the R-algebra C^\infty(X) of smooth functions c : X --> R is a "C-infinity ring". That is, for each smooth function f : R^n --> R there is an n-fold operation \Phi_f : C^\infty(X)^n --> C^\infty(X) acting by \Phi_f: (c_1,...,c_n) |--> f(c_1,...,c_n), and these operations \Phi_f satisfy many natural identities. Thus, C^\infty(X) actually has a far richer structure than the obvious R-algebra structure. We explain a version of algebraic geometry in which rings or algebras are replaced by C-infinity rings. As schemes are the basic objects in algebraic geometry, the new basic objects are "C-infinity schemes", a category of geometric objects generalizing manifolds, and whose morphisms generalize smooth maps. We also discuss "C-infinity stacks", including Deligne-Mumford C-infinity stacks, a 2-category of geometric objects generalizing orbifolds. We study quasicoherent and coherent sheaves on C-infinity schemes and C-infinity stacks, and orbifold strata of Deligne-Mumford C-infinity stacks. This enables us to use the tools of algebraic geometry in differential geometry, and to describe singular spaces such as moduli spaces occurring in differential geometric problems. Many of these ideas are not new: C-infinity rings and C-infinity schemes have long been part of synthetic differential geometry. But we develop them in new directions. In a new book, surveyed in arXiv:1206.4207 and at greater length in arXiv:1208.4948, the author uses C-infinity algebraic geometry to develop a theory of "derived differential geometry", which studies "d-manifolds" and "d-orbifolds", derived versions of smooth manifolds and orbifolds. D-orbifolds will have applications in symplectic geometry, as the geometric structure on moduli spaces of J-holomorphic curves.

Book Source: Digital Library of India Item 2015.46126 dc.contributor.author: Archbold J. W. dc.date.accessioned: 2015-06-26T09:46:00Z dc.date.available: 2015-06-26T09:46:00Z dc.date.citation: 1948 dc.identifier.barcode: 99999990226446 dc.identifier.origpath: /data3/upload/0081/346 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/46126 dc.description.scanningcentre: UOD, Delhi dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 318 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher: Edward Arnold Amp Co. dc.rights: Not Available dc.source.library: Central Library, Delhi University dc.title: Introduction To The Algebraic Geometry Of A Plane

Book Source: Digital Library of India Item 2015.46126 dc.contributor.author: Archbold J. W. dc.date.accessioned: 2015-06-26T09:46:00Z dc.date.available: 2015-06-26T09:46:00Z dc.date.citation: 1948 dc.identifier.barcode: 99999990226446 dc.identifier.origpath: /data3/upload/0081/346 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/46126 dc.description.scanningcentre: UOD, Delhi dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 318 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher: Edward Arnold Amp Co. dc.rights: Not Available dc.source.library: Central Library, Delhi University dc.title: Introduction To The Algebraic Geometry Of A Plane

Book Source: Digital Library of India Item 2015.46126 dc.contributor.author: Archbold J. W. dc.date.accessioned: 2015-06-26T09:46:00Z dc.date.available: 2015-06-26T09:46:00Z dc.date.citation: 1948 dc.identifier.barcode: 99999990226446 dc.identifier.origpath: /data3/upload/0081/346 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/46126 dc.description.scanningcentre: UOD, Delhi dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 318 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher: Edward Arnold Amp Co. dc.rights: Not Available dc.source.library: Central Library, Delhi University dc.title: Introduction To The Algebraic Geometry Of A Plane