Books on the topic 'Moduli spaces of sheaves on surfaces'

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1

Huybrechts, Daniel. The geometry of moduli spaces of sheaves. Braunschweig: Vieweg, 1997.

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2

Manfred, Lehn, ed. The geometry of moduli spaces of sheaves. 2nd ed. Cambridge, UK: Cambridge University Press, 2010.

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3

Huybrechts, Daniel. The geometry of moduli spaces of sheaves. 2nd ed. Cambridge, UK: Cambridge University Press, 2010.

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4

Huybrechts, Daniel, and Manfred Lehn. The Geometry of Moduli Spaces of Sheaves. Wiesbaden: Vieweg+Teubner Verlag, 1997. http://dx.doi.org/10.1007/978-3-663-11624-0.

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5

Hain, Richard M., Eduard Looijenga, and Benson Farb. Moduli spaces of Riemann surfaces. Providence, Rhode Island: American Mathematical Society, 2013.

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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

Göttsche, Lothar. Moduli spaces in algebraic geometry: 2000. Trieste, Italy: ICTP--The Abdus Salam International Centre for Theoretical Physics, 2000.

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8

Casella, Alex. Moduli spaces of real projective structures on surfaces. Tokyo: The Mathematical Society of Japan, 2020.

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9

Bödigheimer, Carl-Friedrich, and Richard M. Hain, eds. Mapping Class Groups and Moduli Spaces of Riemann Surfaces. Providence, Rhode Island: American Mathematical Society, 1993. http://dx.doi.org/10.1090/conm/150.

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10

Izquierdo, Milagros, S. Broughton, Antonio Costa, and Rubí Rodríguez, eds. Riemann and Klein Surfaces, Automorphisms, Symmetries and Moduli Spaces. Providence, Rhode Island: American Mathematical Society, 2014. http://dx.doi.org/10.1090/conm/629.

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11

Schlichenmaier, Martin. An introduction to Riemann surfaces, algebraic curves, and moduli spaces. Berlin: Springer-Verlag, 1989.

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12

Scattone, Francesco. On the compactification of moduli spaces for algebraic K3 surfaces. Providence, R.I: American Mathematical Society, 1987.

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13

An introduction to Riemann surfaces, algebraic curves, and moduli spaces. 2nd ed. Berlin: Springer, 2007.

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14

Hulek, Klaus. Moduli spaces of Abelian surfaces: Compactification, degenerations, and theta functions. Berlin: Walter de Gruyter, 1993.

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15

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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16

D, Drasin, ed. Holomorphic functions and moduli: Proceedings of a workshop held March 13-19, 1986. New York: Springer-Verlag, 1988.

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17

D, Drasin, ed. Holomorphic functions and moduli: Proceedings of a workshop held March 13-19, 1986. New York: Springer-Verlag, 1988.

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18

Rodríguez, Rubí E., 1953- editor of compilation, ed. Riemann and Klein surfaces, automorphisms, symmetries and moduli spaces: Conference in honor of Emilio Bujalance on Riemann and Klein surfaces, symmetries and moduli spaces, June 24-28, 2013, Linköping University, Linköping, Sweden. Providence, Rhode Island: American Mathematical Society, 2014.

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19

The complex analytic theory of Teichmüller spaces. New York: Wiley, 1988.

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20

1956-, Bödigheimer Carl-Friedrich, Hain Richard M. 1953-, and Workshop on Mapping Class Groups and Moduli Spaces of Riemann Surfaces (1991 : Göttingen, Germany, and Seattle, Wash.), eds. Mapping class groups and moduli spaces of Riemann surfaces: Proceedings of workshops held June 24-28, 1991, in Göttingen, Germany, and August 6-10, 1991, in Seattle, Washington ... Providence, R.I: American Mathematical Society, 1993.

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21

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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22

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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23

Xavier, Buff, ed. Espaces de modules des courbes, groupes modulaires et théorie des champs. Paris: Société mathématique de France, 1999.

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24

Tsfasman, M. A. Algebraic geometry codes: Basic notions. Providence, R.I: American Mathematical Society, 2007.

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25

Huybrechts, Daniel, and Manfred Lehn. Geometry of Moduli Spaces of Sheaves. Cambridge University Press, 2010.

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26

Huybrechts, Daniel, and Manfred Lehn. Geometry of Moduli Spaces of Sheaves. Cambridge University Press, 2010.

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27

Huybrechts, Daniel, and Manfred Lehn. Geometry of Moduli Spaces of Sheaves. Cambridge University Press, 2006.

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28

Huybrechts, Daniel, and Manfred Lehn. Geometry of Moduli Spaces of Sheaves. Cambridge University Press, 2010.

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29

Huybrechts, D. K3 Surfaces. Oxford University Press, 2007. http://dx.doi.org/10.1093/acprof:oso/9780199296866.003.0010.

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After abelian varieties, K3 surfaces are the second most interesting special class of varieties. These have a rich internal geometry and a highly interesting moduli theory. Paralleling the famous Torelli theorem, results from Mukai and Orlov show that two K3 surfaces have equivalent derived categories precisely when their cohomologies are isomorphic weighing two Hodge structures. Their techniques also give an almost complete description of the cohomological action of the group of autoequivalences of the derived category of a K3 surface. The basic definitions and fundamental facts from K3 surface theory are recalled. As moduli spaces of stable sheaves on K3 surfaces are crucial for the argument, a brief outline of their theory is presented.
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30

Moduli spaces of stable sheaves on schemes. Tokyo, Japan: The Mathematical Society of Japan, 2016. http://dx.doi.org/10.2969/msjmemoirs/033010000.

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31

Moduli spaces of real projective structures on surfaces. Tokyo, Japan: The Mathematical Society of Japan, 2020. http://dx.doi.org/10.2969/msjmemoirs/038010000.

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32

Schlichenmaier, Martin. Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces. Springer London, Limited, 2007.

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33

Schlichenmaier, Martin. Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces. Springer Berlin / Heidelberg, 2010.

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34

An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-71175-9.

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35

An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0113492.

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36

On the compactification of moduli spaces for algebraic k3 surfaces. 1985.

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37

An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces. Springer Verlag, 1989.

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38

J, Eduard, and Lizhen Ji. Introduction to Moduli Spaces of Riemann Surfaces and Tropical Curves. International Press of Boston, Incorporated, 2017.

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39

Kahn, Constantin, Steven H. Weintraub, and Klaus Hulek. Moduli Spaces of Abelian Surfaces: Compactification, Degenerations and Theta Functions. de Gruyter GmbH, Walter, 2011.

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40

Algebraic Cycles, Sheaves, Shtukas, and Moduli: Impanga Lecture Notes (Trends in Mathematics). Birkhäuser, 2008.

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41

Moduli Spaces of Stable Sheaves on Schemes: Restriction Theorems, Boundedness and the Git Construction. Mathematical Society of Japan, 2016.

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42

Surveys in Differential Geometry, Volume XIV: Geometry of Riemann Surfaces and Their Moduli Spaces. International Press of Boston, Incorporated, 2010.

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43

Moduli spaces of curves, mapping class groups, and field theory. Providence, R.I: American Mathematical Society, 2003.

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44

Santos, Carlos Matheus Silva. Dynamical Aspects of Teichmüller Theory: SL-Action on Moduli Spaces of Flat Surfaces. Springer, 2018.

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45

The Geometry of Moduli Spaces of Sheaves: A Publication of the Max-Planck-Institut für Mathematik, Bonn. Wiesbaden: Vieweg+Teubner Verlag, 1997.

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46

Schlichenmaier, Martin. An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces (Theoretical and Mathematical Physics). 2nd ed. Springer, 2007.

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47

Schlichenmaier, Martin. An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces (Lecture Notes in Physics). Springer, 1989.

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48

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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49

A Celebration of Algebraic Geometry (Clay Mathematics Proceedings). American Mathematical Society, 2013.

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50

Huybrechts, D. Where to Go from Here. Oxford University Press, 2007. http://dx.doi.org/10.1093/acprof:oso/9780199296866.003.0013.

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This chapter gives pointers for more advanced topics, which require prerequisites that are beyond standard introductions to algebraic geometry. The Mckay correspondence relates the equivariant-derived category of a variety endowed with the action of a finite group and the derived category of a crepant resolution of the quotient. This chapter gives the results from Bridgeland, King, and Reid for a special crepant resolution provided by Hilbert schemes and of Bezrukavnikov and Kaledin for symplectic vector spaces. A brief discussion of Kontsevich's homological mirror symmetry is included, as well as a discussion of stability conditions on triangulated categories. Twisted sheaves and their derived categories can be dealt with in a similar way, and some of the results in particular for K3 surfaces are presented.
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