For foliated algebraic surfaces, the paper computes the Zariski decomposition of adjoint divisors K_F+D and gives explicit very-ampleness bounds for their canonical models.
Carnicer, The Poincar\' e problem in the nondicritical case , Annals of mathematics, 140 (2) (1994), 289-294
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Canonical Models of Adjoint Foliated Structures on Surfaces
For foliated algebraic surfaces, the paper computes the Zariski decomposition of adjoint divisors K_F+D and gives explicit very-ampleness bounds for their canonical models.