... Mathematics Index theorems for holomorphic self- maps By Marco Abate, Filippo Bracci, and Francesca Tovena INDEX THEOREMS FOR HOLOMORPHIC SELF- MAPS837whereT1=∂zp∂ˆzhaνf−1z1νf=1∂a∂zj∂∂zp⊗ ... 819–864Index theorems for holomorphic self- mapsBy Marco Abate, Filippo Bracci, and Francesca TovenaIntroductionThe usual index theorems for holomorphic self- maps, like for instancethe classical ... first-order approximation of the zero section of a vector bundle.INDEX THEOREMS FOR HOLOMORPHIC SELF- MAPS829Let us express condition (2.4) in a different way. If (Uα,zα) and (Uβ,zβ)are...