  We characterize the global symmetries for the conjecturally complete
collection of six dimensional superconformal field theories (6D SCFTs) which
are realizable in F-theory and have no frozen singularities. We provide
comprehensive checks of earlier 6D SCFT classification results via an
alternative geometric approach yielding new restrictions which eliminate
certain theories. We achieve this by directly constraining elliptically fibered
Calabi-Yau (CY) threefold Weierstrass models. This allows bypassing all anomaly
cancellation machinery and reduces the problem of classifying the 6D SCFT gauge
and global symmetries realizable in F-theory models before RG-flow to
characterizing features of associated elliptic fibrations involving analysis of
polynomials determining their local models. We supply an algorithm with
implementation producing from a given SCFT base an explicit listing of all
compatible gauge enhancements and their associated global symmetry maxima
consistent with these geometric constraints making explicit the possible
Kodaira type realizations of each algebra summand. In mathematical terms, this
amounts to determining all potentially viable non-compact CY threefold elliptic
fibrations at finite distance in the moduli space with Weil-Petersson metric
meeting certain requirements including transverse pairwise intersection of
singular locus components. We provide local analysis exhausting nearly all CY
consistent transverse singular fiber collisions, global analysis treating all
viable gluings of these local models into larger configurations, and many novel
constraints on singular locus component pair intersections and global fiber
arrangements. We also investigate which transitions between 6D SCFTs can result
from gauging of global symmetries and find that continuous degrees of freedom
can be lost during such transitions.
