For each degree, the moduli space of rational curves on a general Artin-Mumford double solid has exactly two (for lines) or four (higher degrees) irreducible components, giving the first multiple-component verification of Geometric Manin's Conjecture.
Rational curves on Fano threefolds with Gorenstein terminal singularities
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We study the spaces of rational curves on Fano threefolds with Gorenstein terminal singularities. We generalize the results regarding Geometric Manin's Conjecture for smooth Fano threefolds, including the classification of subvarieties with higher a-invariants and Movable Bend-and-Break lemma. We also show Geometric Manin's Conjecture for some singular del Pezzo threefolds.
fields
math.AG 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Moduli spaces of rational curves on Artin-Mumford double solids
For each degree, the moduli space of rational curves on a general Artin-Mumford double solid has exactly two (for lines) or four (higher degrees) irreducible components, giving the first multiple-component verification of Geometric Manin's Conjecture.