Mathematics Colloquia and Seminars

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Stillman's conjecture (recently proved by Ananyan--Hochster) states that the projective dimension of a homogeneous ideal in a polynomial ring admits a bound depending only on the degrees of the generators of
the ideal (and is notably independent of the number of variables). I
will explain joint work with Dan Erman and Steven Sam in which we show that a similar kind of bound holds for any invariant of ideals satisfying two natural conditions (cone-stability and semi-continuity). The key ingredients are the theorem of Ananyan--Hochster and a recent noetherianity result of Draisma.