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<p>We give an explicit formula for the self-intersection number of negative curves on Fermat surfaces. The formula offers us hints to prove the Bounded Negativity Conjecture for the Fermat surfaces by providing explicit negativity bounds, and it also offers the possibility of counterexamples to the conjecture.</p>

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Self-intersection Number of Negative Curves on Fermat Surfaces

  • 期刊论文

  • 发表日期：

    2026年5月27日

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  • Zhenjian Wang

摘要

We give an explicit formula for the self-intersection number of negative curves on Fermat surfaces. The formula offers us hints to prove the Bounded Negativity Conjecture for the Fermat surfaces by providing explicit negativity bounds, and it also offers the possibility of counterexamples to the conjecture.