Classifies irreducible components of Kontsevich moduli spaces for genus one stable maps on degree 4 and 5 del Pezzo threefolds and verifies Geometric Manin's conjecture.
On Varieties of Lines on Linear Sections of Grassmannians
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abstract
General linear sections of codimension 2 of the Grassmannians G(1,4) and G(1,5) appear in the classification of Fano manifolds of high index. Unlike Grassmannians, these manifolds are not homogeneous. Nevertheless, their automorphisms groups have finitely many orbits. In this work we first compute the orbits of these actions. Then we give a description of the variety of lines (under the Pl\"ucker embedding) passing through a fixed point in each orbit of the action. As an application we show that these Fano manifolds are not weakly 2-Fano, completing the classification of weakly 2-Fano manifolds of high index, initiated by Carolina Araujo and Ana-Maria Castravet.
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math.AG 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Moduli space of genus one curves on quartic and quintic del Pezzo threefolds
Classifies irreducible components of Kontsevich moduli spaces for genus one stable maps on degree 4 and 5 del Pezzo threefolds and verifies Geometric Manin's conjecture.