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 smooth h yper- surfaces of low degree
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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.