arXiv subjects

Elaheh Shahsavaripour

Publications and source records attributed to Elaheh Shahsavaripour.

3 recordsLinked to original sources

arXiv2026

Logarithmic Lefschetz fixed point formulae and resonant boundary indices

We study boundary contributions to the holomorphic Lefschetz formula for strict self-maps of compact complex manifolds with a simple normal crossings divisor. At a normally non-resonant boundary fixed point, the local term reduces to the fixed-point problem on the boundary stratum and vanishes in the de Rham specialisation. For resonant points satisfying a normal admissibility condition, finite flat rescaling and relative duality recover the local trace as the coefficient at the excess normal order of a holomorphic family of relative residue traces; in the balanced case, this coefficient is the trace of a class on the special fibre. The numerical coefficient is independent of the admissible presentation. In a coupled family, the de Rham boundary index is the product of the normal contact order and the tangential complete-intersection multiplicity. Boundary contributions to the fixed-point formula for the complement are supported on the resonant fixed points.

math.AG↗

arXiv2026

Excess logarithmic residues for foliations by curves and applications

We introduce excess logarithmic residues for one-dimensional holomorphic foliations tangent to a divisor. They arise from the comparison between the logarithmic normal sheaf and the ordinary normal sheaf of the foliation, and measure the local variation between the logarithmic and classical Baum--Bott contributions. We prove a global residue formula expressing the corresponding Chern numbers as sums of local residues. We then derive a Poincaré-type bound for invariant hypersurfaces from the non-negativity of the relevant logarithmic residues. Finally, for a normal $\mathbb Q$-Gorenstein surface $Y$, we show that the componentwise logarithmic residues of a lifted foliation along the exceptional divisor of a functorial resolution recover the log discrepancies of the singularities of $Y$, giving a dynamical and foliated test for log canonicity of these singularities.

math.AG↗

arXiv2026

Log Bott localization with non-isolated lci zero varieties

We establish a logarithmic Bott localization formula for global holomorphic sections of $T_X(-\log D)$ on a compact complex manifold $X$ with simple normal crossings divisor $D$. The zero scheme is allowed to have non-isolated compact components, assumed to be local complete intersections and to satisfy the natural Bott nondegeneracy condition. We further give a current-theoretic formulation and, in the local complete intersection case, identify the local residue term with a Coleff-Herrera current.

math.CV↗