Modular compactifications of the space of pointed elliptic curves II

DOI10.1112/S0010437X11005549zbMath1260.14033OpenAlexW4256330081MaRDI QIDQ3107320

David Ishii Smyth

Publication date: 23 December 2011

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/s0010437x11005549

zbMATH Keywords

birational geometrylog canonical modelmoduli space of stable curves

Mathematics Subject Classification ID

Families, moduli of curves (algebraic) (14H10) Minimal model program (Mori theory, extremal rays) (14E30) Stacks and moduli problems (14D23)

Related Items (20)

Towards a classification of modular compactifications of \(\mathcal {M}_{g,n}\) ⋮ Moduli of curves, Gröbner bases, and the Krichever map ⋮ Moduli spaces of nonspecial pointed curves of arithmetic genus 1 ⋮ Moduli of abelian covers of elliptic curves ⋮ A classification of modular compactifications of the space of pointed elliptic curves by Gorenstein curves ⋮ A smooth compactification of the space of genus two curves in projective space: via logarithmic geometry and Gorenstein curves ⋮ Modular compactifications of the space of marked trigonal curves ⋮ Reduced invariants from cuspidal maps ⋮ Contracting the Weierstrass locus to a point ⋮ Contractions of subcurves of families of log curves ⋮ Classifying complete \(\mathbb{C}\)-subalgebras of \(\mathbb{C}t\) ⋮ Extremal effective divisors on \(\overline{\mathcal M}_{1,n}\) ⋮ Second flip in the Hassett–Keel program: a local description ⋮ Second flip in the Hassett–Keel program: existence of good moduli spaces ⋮ MODULI OF CURVES WITH NONSPECIAL DIVISORS AND RELATIVE MODULI OF -STRUCTURES ⋮ Intersections of 𝜓-classes on \overline{𝑀}_{1,𝑛}(𝑚) ⋮ A modular compactification of \(\mathcal{M}_{1,n}\) from \(A_ \infty\)-structures ⋮ Modular compactifications of \(\mathcal{M}_{2,n}\) with Gorenstein curves ⋮ A family of divisors on \(\overline{\mathcal{M}}_{g,n}\) and their log canonical models ⋮ A relative GAGA principle for families of curves

Cites Work

• Intersection theory on algebraic stacks and on their moduli spaces
• Calculating cohomology groups of moduli spaces of curves via algebraic geometry
• The irreducibility of the space of curves of a given genus
• Modular compactifications of the space of pointed elliptic curves I
• Deformation Theory
• Divisor classes associated to families of stable varieties, with applications to the moduli space of curves
• Log canonical models for the moduli space of curves: The first divisorial contraction

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