A dual construction for Calabi-Yau complete intersections

Calabi-Yau varieties are objects of great interest in algebraic geometry and also play a significant role in string theory. Their importance is due, among other aspects, to the possibility of constructing pairs of families of varieties that are symmetric under mirror symmetry. When these varieties arise as hypersurfaces in toric Fano varieties, classical results by Batyrev, Berglund-Hübsch-Krawitz, among others, provide constructions of families of Calabi-Yau varieties that are mirror to each other, using the combinatorial features of the underlying varieties. In this talk, we will explain how this theory can be extended to complete intersections, yielding a more general construction that produces new examples of dual families of Calabi-Yau varieties. This is joint work with Michela Artebani (Universidad de Concepción) and Robin Guilbot (Université de Toulouse).