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Tangents to the Nodal Cubic

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If you have a question about this talk, please contact Alexis Marchand.

Given a plane nodal cubic D, how many straight lines are there meeting D in exactly one smooth point? The question can be treated using classical techniques in algebraic geometry which return the correct answer (three). However, just a slight generalisation of this exercise (e.g. the enumeration of higher degree curves maximally tangent to D) renders standard techniques essentially useless. I will introduce Gromov—Witten theory as a framework which allows an efficient discussion of (an obscured version of) such generalised tangent counts and for the nodal cubic we will actually get an explicit formula for these numbers.

This talk is part of the Junior Geometry Seminar series.

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