Inequalities between the Chern numbers of a singular fiber in a family of algebraic curves

Lu, Jun; Tan, Sheng-Li

doi:10.1090/S0002-9947-2012-05625-X

Inequalities between the Chern numbers of a singular fiber in a family of algebraic curves
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by Jun Lu and Sheng-Li Tan PDF

Trans. Amer. Math. Soc. 365 (2013), 3373-3396 Request permission

Abstract:

In a family of curves, the Chern numbers of a singular fiber are the local contributions to the Chern numbers of the total space. We will give some inequalities between the Chern numbers of a singular fiber as well as their lower and upper bounds. We introduce the dual fiber of a singular fiber, and prove a duality theorem. As an application, we will classify singular fibers with large or small Chern numbers.

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