A stability theorem for projective CR manifolds. Issue 5 (4th May 2022)

• Record Type: Journal Article
• Authors: Brinkschulte, Judith; Hill, C. Denson; Nacinovich, Mauro
• Is Part Of: Complex variables and elliptic equations. Volume 67:Issue 5(2022)
• Page Start: 1076
• Page End: 1100
• Publication Date: 2022-05-04
• Subjects: Pseudoconcave CR manifolds -- CR embeddability of abstract CR structures -- stability of embeddings -- projective embeddings; 32V20 -- 32V30 -- 32G07 -- 32F10; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2020.1857371
• Languages: English
• ISSNs: 1747-6933

Abstract

ABSTRACT: We consider smooth deformations of the CR structure of a smooth 2-pseudoconcave compact CR submanifold M of a reduced complex analytic variety X outside the intersection D ∩ M with the support D of a Cartier divisor of a positive line bundle F X . We show that nearby structures still admit projective CR embeddings. Special results are obtained under the additional assumptions that X is a projective space or a Fano variety.