Speaker
Prof.
Michel van Garrel
Description
Condition LSD (log smooth degeneration) states that the pair (Y,D) of Y=Fano and D=smooth anticanonical divisor admits a normal crossings degeneration to a union of blow ups of toric varieties.
Condition HDTV states that Y may be constructed via the HDTV mirror construction, a special case of intrinsic mirror symmetry.
The expectation is that LSD <=> HDTV. Moreover, they imply the existence of an interesting function, shown to be modular in some cases, and special properties of Apéry numbers of Y. Even, there are some hints of links to rationality questions.
Beyond dimension 2, a lot of this remains conjectural at best. Nonetheless, given the confluence of experts, this is an ideal place to discuss some preliminary results and paths forward.
Primary author
Prof.
Michel van Garrel
