| Let X be a complex smooth projective variety of dimension n. We say that is "generalized Lagrangian" if there exist linearly independent global 1-forms \omega_1,\omega_2,...,\omega_{2n}on X such that \omega_1\wedge \omega_2 +\omega_3 \wedge \omega_4 +...+\omega_{2n-1}\wedge \omega_{2n}=0 (as a global 2-form on X) and V=<\omega_1,...,\omega_{2n}> generically generates the cotangent bundle of X. Let \delta (X)=(c_12(X)-2c_2(X))/2 be the degree 2 part of the Chern character of X. If X is generalized Lagrangian and V generates the cotangent budle of X in codimension 1, I will show that \delta(X) is pseudo-effective. More concrete results will be given in the case of surfaces. This is a joint work with Juan C. Naranjo and G. Pietro Pirola. |