相关论文: On the Structure of the Bochner-Martinelli Residue…

We compute residue currents of Bochner-Martinelli type associated with a monomial ideal $I$, by methods involving certain toric varieties. In case the variety of $I$ is the origin, we give a complete description of the annihilator of the…

Using Bochner-Martinelli type residual currents we prove some generalizations of Jacobi's Residue Formula, which allow proper polynomial maps to have `common zeroes at infinity', in projective or toric situations.

We construct Coleff-Herrera products and Bochner-Martinelli type residue currents associated with a tuple $f$ of weakly holomorphic functions, and show that these currents satisfy basic properties from the (strongly) holomorphic case, as…

With a given holomorphic section of a Hermitian vector bundle, one can associate a residue current by means of Cauchy-Fantappi\`e-Leray type formulas. In this paper we define products of such residue currents. We prove that, in the case of…

We study the residue current R^f of Bochner-Martinelli type associated with a tuple f=(f_1,...,f_m) of holomorphic germs at the origin in C^n, whose common zero set equals the origin. Our main results are a geometric description of R^f in…

Given a free resolution of an ideal $J$ of holomorphic functions, one can construct a vector valued residue current $R$, whose annihilator is precisely $J$. In this paper we compute $R$ in case $J$ is a monomial ideal and the resolution is…

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…

We study the weighted Bochner-Martinelli residue current R^p(f) associated with a sequence f=(f_1,...,f_m) of holomorphic germs at the origin in C^n, whose common zero set equals the origin, and p=(p_1,..., p_m)\in N^n. Our main results are…

Let $f_1$, $f_2$, and $f_3$ be holomorphic functions on a complex manifold and assume that the common zero set of the $f_j$ has maximal codimension, i.e., that it is a complete intersection. We prove that the iterated Mellin transform of…

Given a free resolution of an ideal $\mathfrak{a}$ of holomorphic functions, one can construct a vector-valued residue current, $R$, which coincides with the classical Coleff-Herrera product if $\mathfrak{a}$ is a complete intersection…

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…

We construct in complete intersection's case, elementary currents which describe the local ideal, and give a decomposition in it for holomorphic function.

Given a submodule $J\subset \mathcal O_0^{\oplus r}$ and a free resolution of $J$ one can define a certain vector valued residue current whose annihilator is $J$. We make a decomposition of the current with respect to Ass$(J)$ that…

Let $\mathcal{F}^\bullet$ be a complex of coherent $\mathcal{O}_X$-modules over a complex manifold $X$. We give a construction of a residue current associated with this complex that generalizes Andersson and Wulcan's construction of a…

We prove that the Coleff-Herrera residue current, corresponding to a pair of holomorphic functions defining a complete intersection, can be obtained as the unrestricted weak limit of a natural smooth $(0,2)$-form depending on two…

Cohesive module provides a tool to study coherent sheaves on complex manifolds by global analytic methods. In this paper we develop the theory of residue currents for cohesive modules on complex manifolds. In particular we prove that they…

For a Cohen-Macaulay ideal of holomorphic functions, we construct by elementary means residue currents whose annihilator is precisely the given ideal. We give two proofs that the currents have the prescribed annihilator, one using the…

A residue formula is given for the Verlinde formula, which allows one to calculate its coefficients as a polynomial in the level and connects it to the Riemann-Roch formula on the moduli space of vector bundles on a curve.

Given a coherent ideal sheaf $J$ we construct locally a vector-valued residue current $R$ whose annihilator is precisely the given sheaf. In case $J$ is a complete intersection, $R$ is just the classical Coleff-Herrera product. By means of…

Conserved and commuting charges are investigated in both bosonic and supersymmetric classical chiral models, with and without Wess-Zumino terms. In the bosonic theories, there are conserved currents based on symmetric invariant tensors of…