On the moduli space of diffeomorphic algebraic surfaces

• 成果类型: Article
• 署名作者: Manetti, M
• 署名单位: Sapienza University Rome
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s002220000101
• 发表日期: 2001
• 页码: 29-76
• 关键词: deformations; AUTOMORPHISMS; components; functors

摘要

In this paper we show that the number of deformation types of complex structures on a fixed smooth oriented four-manifold can be arbitrarily large. The examples that we consider in this paper are locally simple abelian covers of rational surfaces. The proof involves the algebraic description of rational blowdowns, classical Brill-Noether theory and deformation theory of normal flat abelian covers.