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Monday, August 6, 2018 - 11:35 to 12:35
SMS Seminar Hall
Rahul Kumar Singh
Counting of rational planar curves in $ \mathbb{P}^3 $
Abstract: One of the classical problems in enumerative geometry is to count the number of degree $ d $ rational curves, $ N_d $, in $ \mathbb{P}^2 $, passing through $ 3d-1 $ points. In this talk, we will explain how to obtain a formula for $ N_d $. We will discuss a proof due to Kontsevich-Manin. Finally, we will talk about our recent study of the following problem: What is the number of rational degree $ d $ curves in $ \mathbb{P}^3 $ lying in some plane $ \mathbb{P}^2 $, which satisfy some appropriate conditions. This can be viewed as a family version of the classical problem mentioned above. This is a joint work with Ritwik Mukherjee and Anantadulal Paul.

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