Self-Intersection Formula for Negative Curves on Fermat Surfaces
An explicit formula computing the self-intersection number of a reduced, irreducible negative curve on the complex Fermat surface of degree d greater than or equal to 5, expressed through the degree of an auxiliary plane curve, the Milnor numbers where it meets the Fermat plane curve, and local intersection multiplicities. It yields sufficient conditions under which the Bounded Negativity Conjecture holds for Fermat surfaces and hints at possible counterexamples.
2501.00319
An explicit formula computing the self-intersection number of a reduced, irreducible negative curve on the complex Fermat surface X_d of degree d greater than or equal to 5, expressed through the deg…