On Bott's residue formula for toric complete intersections

2025/06/24 by Peña, Miguel Rodríguez
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.19790

Abstract

We determine the number of singularities - counted whit multiplicities - of generic distributions of dimension and codimension one on smooth complete intersections in compact toric orbifolds with isolated singularities. We also present some applications of this results. First, we analyze the case of regular distributions. As a second application, we establish a Poincaré-type inequality that relates the multidegree of a foliation to the multidegrees of an invariant smooth complete intersection curve.

Citations

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Related

• On codimension one holomorphic distributions on compact toric orbifolds
• Localization in equivariant intersection theory and the Bott residue formula
• Bott's formula and enumerative geometry
• On the Equations Defining Toric L.C.I. Singularities
• Brasselet number and Newton polygons