5 papers
Moduli space of genus one curves on quartic and quintic del Pezzo threefolds
Enhao Feng, Fumiya Okamura
In this article, we study the space of smooth genus one curves on del Pezzo threefolds of degree 4 and 5. We describe the irreducible components of the Kontsevich moduli space gene…
Moduli spaces of rational curves on Artin-Mumford double solids
Fumiya Okamura
We describe the irreducible components of the moduli spaces of rational curves on Artin-Mumford double solids. This provides the first example of Fano varieties that satisfy Geomet…
Rational Curves on Coindex 3 Fano Varieties
Eric Jovinelly, Fumiya Okamura
We describe the moduli space of rational curves on smooth Fano varieties of coindex 3. For varieties of dimension 5 or greater, we prove the moduli space has a single irreducible c…
Rational curves on Fano threefolds with Gorenstein terminal singularities
Fumiya Okamura
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 t…
The irreducibility of the spaces of rational curves on del Pezzo manifolds
Fumiya Okamura
We prove the irreducibility of the spaces of rational curves on del Pezzo manifolds of Picard rank 1 and dimension at least 4 by analyzing the fibers of evaluation maps. As a corol…