Authors conjecture that integral points close in archimedean topology to a fixed rational boundary point on weakly log Fano varieties lie on rational curves with at most two points at infinity, verified on examples.
Manin’s conjecture for integral points on toric varieties
3 Pith papers cite this work. Polarity classification is still indexing.
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Proves asymptotics for integral rational points on a family of degree-one del Pezzo surfaces by reducing the count to correlation sums of binary quadratic and quartic representation numbers analyzed via modular forms.
Proves log Manin's conjecture for Campana rational curves and A1-curves on split toric varieties by combining Cox-ring moduli descriptions with Batyrev-style counting.
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Integral Diophantine approximation on varieties
Authors conjecture that integral points close in archimedean topology to a fixed rational boundary point on weakly log Fano varieties lie on rational curves with at most two points at infinity, verified on examples.
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Counting points on a family of degree one del Pezzo surfaces
Proves asymptotics for integral rational points on a family of degree-one del Pezzo surfaces by reducing the count to correlation sums of binary quadratic and quartic representation numbers analyzed via modular forms.