Sarkisov links from toric weighted blowups of P4 at a point

摘要

We study Sarkisov links initiated by the toric weighted blowup of a point in 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.