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Weak bounded negativity conjecture


Author: Feng Hao
Journal: Proc. Amer. Math. Soc. 147 (2019), 3233-3238
MSC (2010): Primary 14C20, 14J26, 14J99, 14N10
DOI: https://doi.org/10.1090/proc/14376
Published electronically: May 8, 2019
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Abstract: In this paper, we prove the following ``weak bounded negativity conjecture'', which says that given a complex smooth projective surface $ X$, for any reduced curve $ C$ in $ X$ and integer $ g$, assume that the geometric genus of each component of $ C$ is bounded from above by $ g$; then the self-intersection number $ C^2$ is bounded from below.


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Additional Information

Feng Hao
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907

DOI: https://doi.org/10.1090/proc/14376
Received by editor(s): May 3, 2018
Received by editor(s) in revised form: May 8, 2018, August 26, 2018, and August 29, 2018
Published electronically: May 8, 2019
Communicated by: Rachel Pries
Article copyright: © Copyright 2019 American Mathematical Society