Self-intersection of dualizing sheaves of arithmetic surfaces with reducible fibers

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149979Let K be an algebraic number field and O_K the ring of integers of K. Let f : X --> Spec(O_K) be a stable arithmetic surface over O_K of genus g >= 2. In this short note, we will prove that if f has a reducible geometric fiber, then the self intersection of dualizing sheaf of X with Arakelov metric is greater than or equal to log(2)/6(g-1).8 pages, AmS-TeXAlgebraic GeometrySelf-intersection of dualizing sheaves of arithmetic surfaces with reducible fiberstext