Moduli Spaces
Moduli of curves, sheaves, and stable maps.
Moduli Spaces. Moduli of curves, sheaves, and stable maps.
Foundations and canonical references
The standard treatments of moduli spaces approach the subject from complementary angles. Harris, Moduli of Curves (1998) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Mumford, Geometric Invariant Theory (1994) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for moduli spaces include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 1998Moduli of Curvesharris-1998, morrison-1998
- textbook · primary · 1994Geometric Invariant Theorymumford-1994, fogarty-1994, kirwan-1994
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