We study Sarkisov links initiated by the toric weighted blowup of a point in
P3 or P4 using variation of GIT. We completely classify
which of these initiate Sarkisov links and describe the links explicitly.
Moreover, if X is the toric weighted blowup of Pd at a point, we
give a simple criterion in terms of the weights of the blowup that
characterises when X is weak Fano.Comment: 21 pp., Comments are welcom