On the ampleness of the cotangent bundles of complete intersections

• 成果类型: Article
• 署名作者: Xie, Song-Yan
• 署名单位: Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-017-0783-8
• 发表日期: 2018
• 页码: 941-996
• 关键词: meromorphic mappings; VARIETIES; forms

摘要

For the intersection family of general Fermat-type hypersurfaces in defined over an algebraically closed field , we extend Brotbek's symmetric differential forms by a geometric approach, and we further exhibit unveiled families of lower degree symmetric differential forms on all possible intersections of with coordinate hyperplanes. Thereafter, we develop what we call the 'moving coefficients method' to prove a conjecture made by Olivier Debarre: for a generic choice of hypersurfaces of degrees sufficiently large, the intersection has ample cotangent bundle , and concerning effectiveness, the lower bound works. Lastly, thanks to known results about the Fujita Conjecture, we establish the very-ampleness of for all , with a uniform lower bound kappa(0) = 64 (Sigma(c)(i=1) d(i))(2).