Enhanced homotopy theory for period integrals of smooth projective hypersurfaces (Q311077)

The authors endow the middle dimensional primitive cohomology of a smooth projective hypersurface with new interesting structures coming from the Batalin-Vilkovisky algebras and homotopy Lie theory. These structures can be used to give a new perspective on the Hodge filtration and the cup product, as well as on the Griffiths period integrals. As an application, formal families of Calabi-Yau hypersurfaces are studied, in particular their period matrices.