Pingali, VP (2020) A vector bundle version of the Monge-Ampère equation. In: Advances in Mathematics, 360 .
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Abstract
We introduce a vector bundle version of the complex Monge-Ampère equation motivated by a desire to study stability conditions involving higher Chern forms. We then restrict ourselves to complex surfaces, provide a moment map interpretation of it, and define a positivity condition (MA-positivity) which is necessary for the infinite-dimensional symplectic form to be Kähler. On rank-2 bundles on compact complex surfaces, we prove two consequences of the existence of a “positively curved” solution to this equation - Stability (involving the second Chern character) and a Kobayashi-Lübke-Bogomolov-Miyaoka-Yau type inequality. Finally, we prove a Kobayashi-Hitchin correspondence for a dimensional reduction of the aforementioned equation.
| Item Type: | Journal Article |
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| Publication: | Advances in Mathematics |
| Publisher: | Academic Press Inc. |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Keywords: | Kazdan-Warner; Kobayashi-Hitchin correspondence; Moment-map; Vector bundle Monge-Ampère equation; Vortex bundle |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 24 Jan 2023 12:00 |
| Last Modified: | 24 Jan 2023 12:00 |
| URI: | https://eprints.iisc.ac.in/id/eprint/79467 |
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