69 research outputs found
A note on the singularities of residue currents of integrally closed ideals
Given a free resolution of an ideal of holomorpic functions
there is an associated residue current that coincides with the classical
Coleff-Herrera product if is a complete intersection ideal and
whose annihilator ideal equals . In the case when is
an Artinian monomial ideal, we show that the singularities of are small in
a certain sense if and only if is integrally closed.Comment: 9 page
Stabilization of monomial maps
A monomial (or equivariant) selfmap of a toric variety is called stable if
its action on the Picard group commutes with iteration. Generalizing work of
Favre to higher dimensions, we show that under suitable conditions, a monomial
map can be made stable by refining the underlying fan. In general, the
resulting toric variety has quotient singularities; in dimension two we give
criteria for when it can be chosen smooth, as well as examples when it cannot.Comment: To appear in Michigan Math.
Residue currents and cycles of complexes of vector bundles
We give a factorization of the cycle of a bounded complex of vector bundles
in terms of certain associated differential forms and residue currents. This is
a generalization of previous results in the case when the complex is a locally
free resolution of the structure sheaf of an analytic space and it can be seen
as a generalization of the classical Poincar\'e-Lelong formula.Comment: 18 page
Residue currents and fundamental cycles
We give a factorization of the fundamental cycle of an analytic space in
terms of certain differential forms and residue currents associated with a
locally free resolution of its structure sheaf. Our result can be seen as a
generalization of the classical Poincar\'e-Lelong formula. It is also a current
version of a result by Lejeune-Jalabert, who similarly expressed the
fundamental class of a Cohen-Macaulay analytic space in terms of differential
forms and cohomological residues.Comment: 24 page
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