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Handbook of moduli. Volume I. (English) Zbl 1260.14001
Advanced Lectures in Mathematics (ALM) 24. Somerville, MA: International Press; Beijing: Higher Education Press (ISBN 978-1-57146-257-2/pbk; 978-1-57146-265-7/set). xv, 578 p. (2013).

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Publisher’s description: The Handbook of Moduli, comprising three volumes, offers a multi-faceted survey of a rapidly developing subject aimed not just at specialists but at a broad community of producers of algebraic geometry, and even at some consumers from cognate areas. The thirty-five articles in the Handbook, written by fifty leading experts, cover nearly the entire range of the field. They reveal the relations between these many threads and explore their connections to other areas of algebraic geometry, number theory, differential geometry, and topology. The goals of the Handbook are to introduce the techniques, examples, and results essential to each topic, and to say enough about recent developments to provide a gateway to the primary sources. Many articles are original treatments commissioned to bridge gaps in the literature and to make important problems accessible to a wide audience for the first time, and many others illustrate yogas and heuristics that experts use privately to guide intuition or simplify calculation, but that do not appear in published work aimed at other specialists.
This is the first of three volumes constituting the Handbook of Moduli.
The articles of this volume will be reviewed individually. For Vol. II and III see [Zbl 1260.14003; Zbl 1260.14002].
Indexed articles:
Abramovich, Dan; Chen, Qile; Gillam, Danny; Huang, Yuhao; Olsson, Martin; Satriano, Matthew; Sun, Shenghao, Logarithmic geometry and moduli, 1-61 [Zbl 1322.14023]
Brion, Michel, Invariant Hilbert schemes, 64-117 [Zbl 1322.14001]
Caporaso, Lucia, Algebraic and tropical curves: comparing their moduli spaces, 119-160 [Zbl 1322.14045]
Catanese, F., A superficial working guide to deformations and moduli, 161-215 [Zbl 1322.14002]
Do, Norman, Moduli spaces of hyperbolic surfaces and their Weil-Petersson volumes, 217-258 [Zbl 1322.32011]
Edidin, Dan, Equivariant geometry and the cohomology of the moduli space of curves, 259-292 [Zbl 1322.14003]
Faber, C.; Pandharipande, R., Tautological and non-tautological cohomology of the moduli space of curves, 293-330 [Zbl 1322.14046]
Fedorchuk, Maksym; Smyth, David Ishii, Alternate compactifications of moduli spaces of curves, 331-413 [Zbl 1322.14048]
van der Geer, Gerard, The cohomology of the moduli space of abelian varieties, 415-457 [Zbl 1322.14019]
Gritsenko, V.; Hulek, K.; Sankaran, G. K., Moduli of \(K3\) surfaces and irreducible symplectic manifolds, 459-526 [Zbl 1322.14004]
Hain, Richard, Normal functions and the geometry of moduli spaces of curves, 527-578 [Zbl 1322.14049]

MSC:
14-06 Proceedings, conferences, collections, etc. pertaining to algebraic geometry
14-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to algebraic geometry
14D20 Algebraic moduli problems, moduli of vector bundles
14H10 Families, moduli of curves (algebraic)
14K10 Algebraic moduli of abelian varieties, classification
14E30 Minimal model program (Mori theory, extremal rays)
14D15 Formal methods and deformations in algebraic geometry
14K22 Complex multiplication and abelian varieties
00B15 Collections of articles of miscellaneous specific interest
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