Nguyen关于纤维化猜想的新反例  

A New Counterexample to Nguyen’s Conjecture on Surface Fibration

作　　者：蔡文意 肖昊 钱媛媛 卓玲聿 叶昌 CAI Wenyi;XIAO Hao;QIAN Yuanyuan;ZHUO Lingyu;YE Chang(School of Mathematical Sciences, Soochow University, Suzhou 215006, China;School of Science, Huzhou University, Huzhou 313000, China)

机构地区：[1]苏州大学数学科学学院,江苏苏州215006 [2]湖州师范学院理学院,浙江湖州313000

出　　处：《湖州师范学院学报》2019年第8期31-34,共4页Journal of Huzhou University

基　　金：国家自然科学基金项目(11401413);国家级大学生创新创业训练计划项目(201710285014Z)

摘　　要：设f:S→P^1是亏格g的具有三条奇异纤维的曲面纤维化,且其中两条是半稳定的.1998年Nguyen在文献[1]中猜测g≥2时,上述纤维化是不存在的.但2013年龚成在文献[2]中找到了g=2时否定上述猜想的反例.注意到满足上述条件的纤维化具有很强的算术性质,反例重要但数量稀少,并在g=2的情形下对Nguyen的猜想提供了一个新反例.Suppose f:S→P^1 is a surface fibration of genus g with 3 singular fibers and two of the fibers are semistable. In 1998, K. V. Nguyen conjectured that such kind of fibrations do not exist for g≥2. But in 2013, C. Gong, et al found a counterexample to Nguyen’s conjecture for g=2. Noteing that such kind of fibrations show strong arithmetic properties, the counterexamples are important, but they rare in fact. In this paper, a new counterexample to Nguyen’s conjecture for g=2 is constructed.

关 键 词：代数曲面 纤维化 奇异纤维 

分 类 号：O187.1[理学—数学]