The Gorenstein conjecture fails for the tautological ring of

• 成果类型: Article
• 署名作者: Petersen, Dan; Tommasi, Orsola
• 署名单位: Royal Institute of Technology; Leibniz University Hannover
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-013-0466-z
• 发表日期: 2014
• 页码: 139-161
• 关键词: moduli spaces; local systems; eisenstein cohomology; abelian surfaces; CURVES

摘要

We prove that for N equal to at least one of the integers 8, 12, 16, 20 the tautological ring is not Gorenstein. In fact, our N equals the smallest integer such that there is a non-tautological cohomology class of even degree on . By work of Graber and Pandharipande, such a class exists on , and we present some evidence indicating that N is in fact 20.