We study the mixed Hodge theoretic aspects of the B-model side of local mirror symmetry. Our main objectives are to define an analogue of the Yukawa coupling in terms of the variations of the mixed Hodge structures and to study its properties. We also describe a local version of Bershadsky–Cecotti–Ooguri–Vafa’s holomorphic anomaly equation.
"Local B-model and Mixed Hodge Structure." Adv. Theor. Math. Phys. 14 (4) 1089 - 1145, August 2010.