Hodge bundle
“The Hodge bundle (or automorphic bundle), denoted by L (Λ, Γ), is a fundamental fractional (orbifold) line bundle on FΛ(Γ); it is defined as the quotient of OD + Λ (−1) by Γ, where OD+ Λ (−1) is the restriction to D+ Λ of the tautological line bundle on P(ΛC). We recall that L (Λ, Γ) extends to an ample fractional line bundle L ∗(Λ, Γ) on the Baily–Borel compactification FΛ(Γ)∗, and that the sections of mL ∗(Λ, Γ) are precisely the weight-m Γ-automorphic forms. We let λ(Λ, Γ) := c1(L (Λ, Γ)); thus, λ(Λ, Γ) is a Q-Cartier divisor class.” (Laza 和 O’Grady, 2019, p. 1663)