We review here some aspects of our recent works about the geometric
engineering of heterotic little string theories using F-theory. Building on the
seminal work by Aspinwall and Morrison as well as Intrilligator and Blum, we
solve some longstanding open questions thanks to recent progress in our
understanding of 6D (1,0) theories and their generalized symmetries. On the
geometry side, these systems correspond to non-compact elliptically fibered
Calabi-Yau varieties that must admit the structure of an elliptic K3 fibration.
From fiberwise F-theory/Heterotic duality the K3 plays a central role - it
determines the 6D flavor group, as well as different T-dual LSTs via
inequivalent elliptic fibration structures. The geometries we obtain are some
finer versions of Kulikov degenerations: the point where the K3 fiber
degenerates is the locus where the LST arises. This structure serve on one hand
to check our field theory predictions on LST dualities via the match of Coulomb
branch dimension, flavor symmetries, and 2-group structure constants, and also
on the other hand to deduce novel LST models and their networks of dualities,
thus allowing exploring non-geometric Heterotic regimes.Comment: Contribution to the proceedings of String Math 202