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We prove the irreducibility of moduli spaces of rational curves on a general del Pezzo threefold of Picard rank 1 and degree 1. As corollaries, we confirm Geometric Manin’s conjecture and enumerativity of certain Gromov–Witten invariants for these threefolds.
Motivated by potential applications in network theory, engineering and computer science, we study r-ample simplicial complexes. These complexes can be viewed as finite approximations to the Rado complex which has a remarkable property of indestructibility, in the sense that removing any finite...
Let M be an irreducible compact hyperkähler manifold of complex dimension six. Under an assumption on the Looijenga–Lunts–Verbitsky decomposition of the cohomology of M, we prove that the second Betti number of M is at most 23.
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