Chern slopes of simply connected complex surfaces of general type are dense in [2,3]

• 成果类型: Article
• 署名作者: Roulleau, Xavier; Urzua, Giancarlo
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2015.182.1.6
• 发表日期: 2015
• 页码: 287-306
• 关键词: algebraic-surfaces; numbers; geography

摘要

We prove that for any number r is an element of [2,3], there are spin (resp. non-spin and minimal) simply connected complex surfaces of general type X with c(1)(2)(X)/c(2)(X) arbitrarily close to r. In particular, this shows the existence of simply connected surfaces of general type arbitrarily close to the Bogomolov-Miyaoka-Yau line. In addition, we prove that for any r is an element of [1,3] and any integer q >= 0, there are minimal complex surfaces of general type X with C-1(2)(X)/c(2)(X) arbitrarily close to r and 71(X) isomorphic to the fundamental group of a compact Riemann surface of genus q.