29 Aug 2019
•
Felten Simon
•
Filip Matej
•
Ruddat Helge
We prove the existence of a smoothing for a toroidal crossing space under
mild assumptions. By linking log structures with infinitesimal deformations,
the result receives a very compact form for normal crossing spaces...The main
approach is to study log structures that are incoherent on a subspace of
codimension two and prove a Hodge to de Rham degeneration theorem for such log
spaces. We show that new developments of Bogomolov-Tian-Todorov theory can be
applied to obtain smoothings. The theory relates to recent work in mirror
symmetry and the construction of Frobenius manifold structures. It has
potential applications to the classification of Fano fourfolds.(read more)