A Recursive Formula for Osculating Curves

Abstract: Let $X$ be a smooth complex projective variety. Using a construction devised to Gathmann, we present a recursive formula for some of the Gromov-Witten invariants of $X$. We prove that, when $X$ is homogeneous, this formula gives the number of osculating rational curves at a general point of a general hypersurface of $X$. This generalizes the classical well known pairs of in inflection (asymptotic) lines for surfaces in $\mathbb{P}^3$ of Salmon, as well as Darboux's 27 osculating conics.

algebraic geometry

Audience: researchers in the topic

Comments: Link for the talk will be provided a few days in advance.

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Brazilian algebraic geometry seminar

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