The University of Arizona
Please note that this event has been cancelled!

Enumeration of singular subvarieties with tangency conditions

[CANCELLED] Enumeration of singular subvarieties with tangency conditions

Series: Algebraic Geometry Seminar
Location: ENR 2 S395
Presenter: Yu-jong Tzeng, University of Minnesota

How many nodal degree d plane curves are tangent to a given line? The celebrated Caporaso-Harris recursion formula gives a complete answer for any number of nodes, degrees, and all possible tangency conditions. In this talk, I will report my recent work on the generalization of the counting problem to singular subvarieties with given tangency condition to a fixed smooth divisor on any smooth varieties. I will relate the enumeration to tautological integrals on Hilbert schemes of points and show the numbers of curves in question are given by universal polynomials. As a result, we can obtain infinitely many new formulas for nodal curves and understand the asymptotic behavior for all singular curves with any tangency conditions. 

 

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