2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167397Using lattice theory, we establish a one-to-one correspondence between the set of Fourier-Mukai partners of a projective $K3$ surface and the set of 0-dimensional standard cusps of its Kahler moduli. We also study the relation between twisted Fourier-Mukai partners and general 0-dimensional cusps, and the relation between Fourier-Mukai partners with elliptic fibrations and certain 1-dimensional cusps.25 pages. I corrected a mistakeAlgebraic GeometryMathematical Physics14J28text