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Auteur : Grafiati

Publié le 14 mars 2023

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1

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

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2

Manfred, Lehn, dir. The geometry of moduli spaces of sheaves. 2^e éd. Cambridge, UK : Cambridge University Press, 2010.

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3

service), SpringerLink (Online, dir. Lectures on Algebraic Geometry I : Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces. 2^e éd. Wiesbaden : Vieweg+Teubner Verlag / Springer Fachmedien Wiesbaden GmbH, Wiesbaden, 2012.

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4

Huybrechts, Daniel. The geometry of moduli spaces of sheaves. 2^e éd. Cambridge, UK : Cambridge University Press, 2010.

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5

service), SpringerLink (Online, dir. Lectures on algebraic geometry. Wiesbaden : Vieweg, 2008.

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6

Carruth, M. R. Surface voltage gradient role in high voltage solar array/plasma interactions. [Marshall Space Flight Center, Ala.] : National Aeronautics and Space Administration, George C. Marshall Space Flight Center, 1985.

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7

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

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8

Nurwantoro, Pekik. A theoretical study of the surface nucleation field at H[inferior C3] and of superconducting surface sheaths in isotropic type-II superconductors. Birmingham : University of Birmingham, 1998.

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9

Pandharipande, Rahul. Maps, Sheaves and K3 Surfaces. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198784913.003.0005.

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The conjectural equivalence of curve counting on Calami- Yau 3-folds via stable maps and stable pairs is discussed. By considering Cali-Yau 3-folds with K3 fibrations, the correspondence naturally connects curve and sheaf counting on K3 surfaces. New conjectures (with D. Maulik) about descendent integration on K3 surfaces are announced. The proof of the complete Yau-Zaslow conjecture is surveyed.

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10

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

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11

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

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12

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

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13

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

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14

Diederich, Klas, et Günter Harder. Lectures on Algebraic Geometry I : Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces. Springer Fachmedien Wiesbaden GmbH, 2013.

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15

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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16

Krug, Andreas. Extension Groups of Tautological Sheaves on Hilbert Schemes of Points on Surfaces. Logos Verlag Berlin, 2012.

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17

Huybrechts, D. Fourier-Mukai Transforms in Algebraic Geometry. Oxford University Press, 2007. http://dx.doi.org/10.1093/acprof:oso/9780199296866.001.0001.

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This book provides a systematic exposition of the theory of Fourier-Mukai transforms from an algebro-geometric point of view. Assuming a basic knowledge of algebraic geometry, the key aspect of this book is the derived category of coherent sheaves on a smooth projective variety. The derived category is a subtle invariant of the isomorphism type of a variety, and its group of autoequivalences often shows a rich structure. As it turns out — and this feature is pursued throughout the book — the behaviour of the derived category is determined by the geometric properties of the canonical bundle of the variety. Including notions from other areas, e.g., singular cohomology, Hodge theory, abelian varieties, K3 surfaces; full proofs and exercises are provided. The final chapter summarizes recent research directions, such as connections to orbifolds and the representation theory of finite groups via the McKay correspondence, stability conditions on triangulated categories, and the notion of the derived category of sheaves twisted by a gerbe.

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18

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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19

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

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