Schemes of rational curves on Del Pezzo surfaces

Abstract: Schemes parametrizing rational curves on a projective variety have a natural partition in terms of the degrees of the rational curves. In this talk, we present a natural refinement of this partition on schemes parametrizing rational curves on Del Pezzo surfaces. The classical description of Del Pezzo surfaces as blow-ups of the projective plane at points in general position yields that these refined partitions reflect the multiplicity of the rational curves at each of the blown-up points. Moreover, we compute the dimension of components of these parameter spaces containing (points corresponding to) resolutions of plane curves which are singular at the blown-up points.

algebraic geometry

Audience: researchers in the topic

Brazilian algebraic geometry seminar

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