Searcharxiv⌕ Search

arXiv subjects

Fumiya Okamura

Publications and source records attributed to Fumiya Okamura.

5 recordsLinked to original sources
arXiv2026

Moduli space of genus one curves on quartic and quintic del Pezzo threefolds

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 generically parametrizing genus one stable maps with irreducible domains and classify the irreducible components of the morphism space from general elliptic curves. Our result verifies the Geometric Manin's conjecture for all del Pezzo threefolds of degree 4 and 5 over the complex numbers.

math.AG↗
arXiv2025

Rational curves on Fano threefolds with Gorenstein terminal singularities

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.

math.AG↗
arXiv2025

Moduli spaces of rational curves on Artin-Mumford double solids

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 Geometric Manin's Conjecture with multiple Manin components in moduli space of rational curves for each degree.

math.AG↗
arXiv2024

Rational Curves on Coindex 3 Fano Varieties

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 component for each effective numerical class of curves. For varieties of dimension 4, we describe families of rational curves in terms of Fujita's $a$-invariant. Our results verify Lehmann and Tanimoto's Geometric Manin's Conjecture for all smooth coindex 3 Fano varieties over the complex numbers.

math.AG↗