| Given a smooth projective algebraic variety X and a point P on X, one can consider a number m(X, O_X(1), P) (call it mobility threshold), which, in a sense, is an “average multiplicity” at P of irreducible zero loci of various global sections of O_X(m) and big enough m. The number m(X, O_X(1), P), despite its known counterparts such as, say, Seshadri constants and several other asymptotic invariants of X, has not been studied so far. The aim of the talk is to motivate such a study (or, at least, point out several perspectives from which such a study might be reasonable and interesting). |