649 research outputs found

    Expected resurgences and symbolic powers of ideals

    Get PDF
    We give explicit criteria that imply the resurgence of a self-radical ideal in a regular ring is strictly smaller than its codimension, which in turn implies that the stable version of Harbourne's conjecture holds for such ideals. This criterion is used to give several explicit families of such ideals, including the defining ideals of space monomial curves. Other results generalize known theorems concerning when the third symbolic power is in the square of an ideal, and a strong resurgence bound for some classes of space monomial curves.Comment: Final version to appear in the Journal of the London Mathematical Societ

    Bounding symbolic powers via asymptotic multiplier ideals

    Full text link
    We revisit a bound on symbolic powers found by Ein-Lazarsfeld-Smith and subsequently improved by Takagi-Yoshida. We show that the original argument of Ein-Lazarsfeld-Smith actually gives the same improvement. On the other hand, we show by examples that any further improvement based on the same technique appears unlikely. This is primarily an exposition; only some examples and remarks might be new.Comment: 10 pages. Primarily exposition. Originally written as appendix to lecture notes by Brian Harbourne. v2: Minor changes. v3: Final version, appeared in Ann. Univ. Pedagog. Crac. Stud. Mat

    Segre Class Computation and Practical Applications

    Full text link
    Let X⊂YX \subset Y be closed (possibly singular) subschemes of a smooth projective toric variety TT. We show how to compute the Segre class s(X,Y)s(X,Y) as a class in the Chow group of TT. Building on this, we give effective methods to compute intersection products in projective varieties, to determine algebraic multiplicity without working in local rings, and to test pairwise containment of subvarieties of TT. Our methods may be implemented without using Groebner bases; in particular any algorithm to compute the number of solutions of a zero-dimensional polynomial system may be used
    • …
    corecore