The polynomial method over varieties

• 成果类型: Article
• 署名作者: Walsh, Miguel N.
• 署名单位: University of Buenos Aires; University of Buenos Aires; Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-020-00975-6
• 发表日期: 2020
• 页码: 469-512
• 关键词: connected components; number; points; CURVES; bounds

摘要

We establish sharp estimates that adapt the polynomial method to arbitrary varieties. These include a partitioning theorem, estimates on polynomials vanishing on fixed sets and bounds for the number of connected components of real algebraic varieties. As a first application, we provide a general incidence estimate that is tight in its dependence on the size, degree and dimension of the varieties involved.