Orders of vanishing and U(1) charges in F-theory

A bstract Many interesting questions about F-theory models, including several concerning the swampland, involve massless matter charged under U(1) gauge symmetries. It is therefore important to better understand geometric properties of models realizing various charges. We propose that, for described by elliptic fibrations in Weierstrass form, charge light encoded orders vanishing section components corresponding symmetry. give specific equations relating charges that seem hold both U(1)-charged singlets and additionally a simply-laced nonabelian algebra. Our formulas correctly describe prior literature, we an argument they should arbitrarily high They also resemble p -adic valuations divisibility sequences developed Stange [1]. These proposals could serve as analogue Katz-Vafa method, allowing one determine without resolution. Additionally, predict information with general charges, which may be useful exploring landscape swampland.