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arxiv: 1107.3824 · v1 · pith:R7EIDG4Ynew · submitted 2011-07-19 · 🧮 math.AG · math.NT

Asymptotic behaviour of rational curves

David Bourqui (IRMAR) This is my paper
classification 🧮 math.AG math.NT
keywords behaviourcaserationalasympoticasymptoticbecomescoordinatecrucial
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We investigate the asympotic behaviour of the moduli space of morphisms from the rational curve to a given variety when the degree becomes large. One of the crucial tools is the homogeneous coordinate ring of the variey. First we explain in details what happens in the toric case. Then we examine the general case.

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    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.