Stable pair, tropical, and log canonical compact moduli of del Pezzo surfaces

Abstract

We give a functorial normal crossing compactification of the moduli of smooth marked cubic surfaces entirely analogous to the Grothendieck-Knudsen compactification $M_{0,n}\subset {\bar{M}}_{0,n}$.

49 pages, 8 figures. v2: Added section 3 "Iitaka fibration for subvarieties of algebraic tori"

References in corpus (3)

• Inversion of adjunction on log canonicity
• Tropical varieties for non-archimedean analytic spaces
• Bergman Complexes, Coxeter Arrangements, and Graph Associahedra

Cited by in corpus (30)

• Equations of tropical varieties
• Monodromy Filtrations and the Topology of Tropical Varieties
• Intersection Theory on Tropicalizations of Toroidal Embeddings
• Tropical geometry of moduli spaces of weighted stable curves
• Pluricanonical maps of stable log surfaces
• Elimination Theory for Tropical Varieties
• The Universal Kummer Threefold
• Sagbi Bases of Cox-Nagata Rings
• Moduli of cubic surfaces and their anticanonical divisors
• Tropical Intersection Theory from Toric Varieties
• Coble fourfold, $S_6$-invariant quartic threefolds, and Wiman-Edge sextics
• Moduli of products of stable varieties
• Anticanonical tropical cubic del Pezzos contain exactly 27 lines
• Non-isomorphic smooth compactifications of the moduli space of cubic surfaces
• The Picard group of the moduli of smooth complete intersections of two quadrics
• Stable pair compactifications of the moduli space of degree one del pezzo surfaces via elliptic fibrations
• Exceptional Loci on ${\bar{M}}_{0,n}$ and Hypergraph Curves
• Tropical convexity in location problems
• Tropicalization of Del Pezzo Surfaces
• On Tropical Compactifications
• Homology of tropical varieties
• Wonderful compactifications and rational curves with cyclic action
• Intersection Theory on Linear Subvarieties of Toric Varieties
• The moduli space of cubic surface pairs via the intermediate Jacobians of Eckardt cubic threefolds
• Compactifications of moduli of del Pezzo surfaces via line arrangement and K-stability
• Moduli Spaces of Rational Graphically Stable Curves
• Comparison Theorems of Phylogenetic Spaces and the Moduli Spaces of Curves
• Rigid curves on ${\bar{M}}_{0,n}$ and arithmetic breaks
• Frobenius actions on Del Pezzo surfaces of degree 2
• Initial degenerations of flag varieties