Everything about Moduli space
Geometric space whose points represent algebro-geometric objects of some fixed kind
In mathematics, in particular algebraic geometry, a moduli space is a geometric space whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects. Such spaces frequently arise as solutions to classification problems: If one can show that a collection of interesting objects can be given the structure of a geometric space, then one can parametrize such objects by introducing coordinates on the resulting space. In this context, the term "modulus" is used synonymously with "parameter"; moduli spaces were first understood as spaces of parameters rather than as spaces of objects. A variant of moduli spaces is formal moduli. Bernhard Riemann first used the term "moduli" in 1857. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Moduli spaceA 5-minute orientation
- Skim a recent paper: Relativistic moduli space for kink collisionsInfluential work since 2022
- Pick up a classic book: Moduli spaces and vector bundlesThe most-reprinted book on the subject
- Read the landmark paper: Moduli space of Calabi-Yau manifoldsCited 393 times
- Go sideways: Stack (mathematics)A closely related topic
- Go sideways: Deligne–Mumford stackA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Moduli space of Calabi-Yau manifolds
Duality in Calabi-Yau moduli space
Moduli Space of Non-Abelian Vortices
Averaging over Narain moduli space
Moduli space of BPS domain walls
Lectures on strings and moduli space
The moduli space of stable quotients
Topological gravity and moduli space
🆕 Influential since 2022
📚 Books worth reading
Moduli spaces and vector bundlesSteven B. Bradlow, S. Ramanan · 2009
Geometric invariant theoryDavid Mumford, John Fogarty · 1965
Graphs on surfaces and their applicationsS. K. Lando, Sergei K. Lando · 2003
Frobenius manifolds and moduli spaces for singularitiesClaus Hertling · 2002
Algebraic geometry codesM. A. Tsfasman, Michael Tsfasman · 2007- 📕Existenz semiuniverseller Deformationen in der komplexen AnalysisHarald Stieber · 1988
- 📕Sur la classification des courbes gauchesMireille Deschamps · 1990
Fukuso tayōtaironKunihiko Kodaira · 1986
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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