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Geometry & Topology Seminar

Title: The Demailly systems with vortex ansatz
Speaker: Arindam Mandal (IISc)
Date: 16 October 2023
Time: 4:00 pm
Venue: LH-1

Given a Hermitian holomorphic vector bundle of arbitrary rank on a projective manifold, we can define the notions of Nakano positivity, Griffiths positivity and ampleness. All these notions of positivity are equivalent for line bundles. In general, Nakano positivity implies Griffiths positivity and Griffiths positivity implies ampleness. A conjecture due to Griffiths says that ampleness implies Griffiths positivity. To prove the equivalence between Griffiths positivity and ampleness, Demailly designed several systems of equations of Hermitian-Yang-Mills type for the curvature tensor. In this talk, I will briefly discuss about the solution of these systems on the vortex bundle using method of continuity.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 24 Jun 2024