+91-674-249-4082

Submitted by klpatra on 1 August, 2018 - 09:16

Date/Time:

Monday, August 6, 2018 - 11:35 to 12:35

Venue:

SMS Seminar Hall

Speaker:

Rahul Kumar Singh

Affiliation:

NISER

Title:

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.

**School of Mathematical Sciences**

NISER, PO- Bhimpur-Padanpur, Via- Jatni, District- Khurda, Odisha, India, PIN- 752050

Tel: +91-674-249-4081

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