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Zeta functions and Bernstein-Sato polynomials for ideals in dimension two
Zeta functions Bernstein-Sato polynomials ideals dimension two
2011/2/28
For a nonzero ideal I ⊳C[x1, . . . , xn], with 0 ∈ supp I, a (general-ized) conjecture of Igusa–Denef–Loeser predicts that every pole of its topologi-cal zeta function is a root of its Bernstein...
Generalizing Tanisaki's ideal via ideals of truncated symmetric functions
Generalizing Tanisaki's ideal ideals of truncated symmetric functions
2011/1/19
We de ne a family of ideals Ih in the polynomial ring Z[x1; x2; : : : ; xn] that are
parametrized by Hessenberg functions h (equivalently Dyck paths or ample partitions). The
ideals Ih generalize al...
Normality of Monomial Ideals
Normality Monomial Ideals
2010/11/30
Given the monomial ideal I = (x 1 1 , . . . , x n n ) K[x1, . . . , xn] where i are positive integers and K a field and let J be the integral closure of I . It is a challenging problem to translat...
Stanley conjecture on intersections of four monomial prime ideals
Monomial Ideals Stanley decompositions Stanley depth
2010/12/14
We show that the Stanley’s Conjecture holds for an intersection of four monomial prime ideals of a polynomial algebra S over a field and for an arbitrary intersection of monomial prime ideals (Pi)i∈[s...