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Books on the topic 'Moduli space of vector bundles'

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Published: 14 March 2023

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1

Brambila-Paz, Leticia, Steven B. Bradlow, Oscar Garcia-Prada, and S. Ramanan, eds. Moduli Spaces and Vector Bundles. Cambridge: Cambridge University Press, 2009. http://dx.doi.org/10.1017/cbo9781139107037.

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2

1957-, Bradlow Steve, ed. Moduli spaces and vector bundles. Cambridge: Cambridge University Press, 2009.

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3

Alexeev, Valery, Angela Gibney, Elham Izadi, János Kollár, Eduard Looijenga, Valery Alexeev, Angela Gibney, Elham Izadi, János Kollár, and Eduard Looijenga, eds. Compact Moduli Spaces and Vector Bundles. Providence, Rhode Island: American Mathematical Society, 2012. http://dx.doi.org/10.1090/conm/564.

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4

Alexeev, Valery. Compact moduli spaces and vector bundles: Conference on compact moduli and vector bundles, October 21-24, 2010, University of Georgia, Athens, Georgia. Providence, R.I: American Mathematical Society, 2012.

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5

Clay Mathematics Institute Workshop on Moduli Spaces of Vector Bundles, with a View toward Coherent Sheaves (2006 Cambridge, Mass.). Grassmannians, moduli spaces, and vector bundles: Clay Mathematics Institute Workshop on Moduli Spaces of Vector Bundles, with a View towards Coherent Sheaves, October 6-11, 2006, Cambridge, Massachusetts. Edited by Ellwood D. (David) 1966- and Previato Emma. Providence, RI: American Mathematical Society, 2011.

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6

1776-1853, Hoene-Wroński Józef Maria, and Pragacz Piotr, eds. Algebraic cycles, sheaves, shtukas, and moduli. Basel: Birkhäuser, 2008.

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7

1944-, Maruyama Masaki, and International Taniguchi Symposium (35th : 1994 : Sanda-shi, Japan), eds. Moduli of vector bundles. New York: M. Dekker, 1996.

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8

Moduli spaces and arithmetic dynamics. Providence, R.I: American Mathematical Society, 2012.

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9

School and Workshop on Vector Bundles and Low Codimensional Varieties (2006 Trento, Italy). Vector bundles and low codimensional subvarieties: State of the art and recent developments. [Roma]: Aracne, 2007.

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10

Potier, Joseph Le. Systèmes cohérents et structures de niveau. Paris: Société Mathématique de France, 1993.

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11

Potier, Joseph Le. Systèmes cohérents et structures de niveau. Montrouge: Société mathématique de France, 1993.

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12

editor, Donagi Ron, Katz Sheldon 1956 editor, Klemm Albrecht 1960 editor, and Morrison, David R., 1955- editor, eds. String-Math 2012: July 16-21, 2012, Universität Bonn, Bonn, Germany. Providence, Rhode Island: American Mathematical Society, 2015.

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13

Pan-American Advanced Studies Institute (2009 Universidade Federal de Pernambuco). Commutative algebra and its connections to geometry: Pan-American Advanced Studies Institute, August 3--14, 2009, Universidade Federal de Pernambuco, Olinda, Brazil. Edited by Corso Alberto and Polini Claudia 1966-. Providence, R.I: American Mathematical Society, 2011.

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14

Ramanan, S., Steven B. Bradlow, Oscar García-Prada, and Leticia Brambila-Paz. Moduli Spaces and Vector Bundles. Cambridge University Press, 2011.

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15

Ramanan, S., Steven B. Bradlow, Oscar García-Prada, and Leticia Brambila-Paz. Moduli Spaces and Vector Bundles. Cambridge University Press, 2011.

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16

Ramanan, S., Steven B. Bradlow, Oscar García-Prada, and Leticia Brambila-Paz. Moduli Spaces and Vector Bundles. Cambridge University Press, 2009.

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17

Maruyama, M. Moduli Spaces of Vector Bundles. Cambridge University Press, 2004.

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18

Ramanan, S., Steven B. Bradlow, Oscar García-Prada, and Leticia Brambila-Paz. Moduli Spaces and Vector Bundles. Cambridge University Press, 2009.

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19

Poritz, Jonathan Adam. The moduli space of stable vector bundles on a punctured Riemann surface. 1992.

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20

Geometry, Topology, and Physics of Moduli Spaces of Higgs Bundles. World Scientific Publishing Co Pte Ltd, 2018.

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21

Betti Numbers of the Moduli Space of Rank 3 Parabolic Higgs Bundles (Memoirs of the American Mathematical Society). Amer Mathematical Society, 2007.

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22

Maruyama, Masaki. Moduli of Vector Bundles. Taylor & Francis Group, 2018.

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23

Belmans, Pieter, Wei Ho, and Aise Johan de Jong, eds. Stacks Project Expository Collection. Cambridge University Press, 2022. http://dx.doi.org/10.1017/9781009051897.

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The Stacks Project Expository Collection (SPEC) compiles expository articles in advanced algebraic geometry, intended to bring graduate students and researchers up to speed on recent developments in the geometry of algebraic spaces and algebraic stacks. The articles in the text make explicit in modern language many results, proofs, and examples that were previously only implicit, incomplete, or expressed in classical terms in the literature. Where applicable this is done by explicitly referring to the Stacks project for preliminary results. Topics include the construction and properties of important moduli problems in algebraic geometry (such as the Deligne–Mumford compactification of the moduli of curves, the Picard functor, or moduli of semistable vector bundles and sheaves), and arithmetic questions for fields and algebraic spaces.

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24

Farb, Benson, and Dan Margalit. Moduli Space. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691147949.003.0013.

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This chapter focuses on the moduli space of Riemann surfaces. The moduli space parameterizes many different kinds of structures on Sɡ, such as isometry classes of hyperbolic structures on S, conformal classes of Riemannian metrics on S, biholomorphism classes of complex structures on S, and isomorphism classes of smooth algebraic curves homeomorphic to S. The chapter first considers the moduli space as the quotient of Teichmüller space before discussing the moduli space of the torus. It then examines the theorem (due to Fricke) that Mod(S) acts properly discontinuously on Teich(S), with a finite-index subgroup of Mod(S) acting freely such that M(S) is finitely covered by a smooth aspherical manifold. The chapter also looks at Mumford's compactness criterion, which describes what it means to go to infinity in M(S), and concludes by showing that M(Sɡ) is very close to being a classifying space for Sɡ-bundles.

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25

Mochizuki, Takuro. Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor $D$-Modules, Part 2 (Memoirs of the American Mathematical Society) (Memoirs of the American Mathematical Society). American Mathematical Society, 2006.

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26

Mann, Peter. Linear Algebra. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0037.

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This chapter is key to the understanding of classical mechanics as a geometrical theory. It builds upon earlier chapters on calculus and linear algebra and frames theoretical physics in a new and useful language. Although some degree of mathematical knowledge is required (from the previous chapters), the focus of this chapter is to explain exactly what is going on, rather than give a full working knowledge of the subject. Such an approach is rare in this field, yet is ever so welcome to newcomers who are exposed to this material for the first time! The chapter discusses topology, manifolds, forms, interior products, pullback and pushforward, as well as tangent bundles, cotangent bundles, jet bundles and principle bundles. It also discusses vector fields, integral curves, flow, exterior derivatives and fibre derivatives. In addition, Lie derivatives, Lie brackets, Lie algebra, Lie–Poisson brackets, vertical space, horizontal space, groups and algebroids are explained.

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27

Mann, Peter. Differential Geometry. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0038.

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This chapter is key to the understanding of classical mechanics as a geometrical theory. It builds upon earlier chapters on calculus and linear algebra and frames theoretical physics in a new and useful language. Although some degree ofmathematical knowledge is required (from the previous chapters), the focus of this chapter is to explain exactlywhat is going on, rather than give a full working knowledge of the subject. Such an approach is rare in this field, yet is ever so welcome to newcomers who are exposed to this material for the first time! The chapter discusses topology, manifolds, forms, interior products, pullback and pushforward, as well as tangent bundles, cotangent bundles, jet bundles and principle bundles. It also discusses vector fields, integral curves, flow, exterior derivatives and fibre derivatives. In addition, Lie derivatives, Lie brackets, Lie algebra, Lie–Poisson brackets, vertical space, horizontal space, groups and algebroids are explained.

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28

McDuff, Dusa, and Dietmar Salamon. Linear symplectic geometry. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198794899.003.0003.

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The second chapter introduces the basic concepts of symplectic topology in the linear algebra setting, such as symplectic vector spaces, the linear symplectic group, Lagrangian subspaces, and the Maslov index. In the section on linear complex structures particular emphasis is placed on the homotopy equivalence between the space of symplectic forms and the space of linear complex structures. The chapter includes sections on symplectic vector bundles and the first Chern class.

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29

Farb, Benson, and Dan Margalit. A Primer on Mapping Class Groups (PMS-49). Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691147949.001.0001.

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The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students. It begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn–Nielsen–Baer–theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmüller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification.

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30

Algebraic And Geometric Aspects Of Integrable Systems And Random Matrices Ams Special Session Algebraic And Geometric Aspects Of Integrable Systems And Random Matrices January 67 2012 Boston Ma. American Mathematical Society, 2013.

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31

Quiver Representations and Quiver Varieties. American Mathematical Society, 2016.

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32

Hilbert Schemes of Points and Infinite Dimensional Lie Algebras. American Mathematical Society, 2018.

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33

Surveys on Recent Developments in Algebraic Geometry. American Mathematical Society, 2017.

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34

Integrability, Quantization, and Geometry. American Mathematical Society, 2021.

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