Segre numbers, a generalized King formula , and local intersections

Mats Andersson (1) , Hakan Samuelsson (1) , Elizabeth Wulcan (2) , Alain Yger (3)

1 Department of Mathematical Sciences
2 Department of Mathematics
3 IMB - Institut de Mathématiques de Bordeaux

Let $J$ be an ideal sheaf on a reduced analytic space $X$ with zero set $Z$. We show that the Lelong numbers of the restrictions to $Z$ of certain generalized Monge-Amp ere products ($dd^c log |f|^2)^k$, where $f$ is a tuple of generators of $J$ , coincide with the so-called Segre numbers of $J$ , introduced independently by Tworzewski and Ga ffney-Gassler. More generally we show that these currents satisfya generalization of the classical King formula that takes into account fixed andmoving components of Vogel cycles associated with $J$ . A basic tool is a new calculusfor products of positive currents of Bochner-Martinelli type. We also discussconnections to intersection theory.

Domaines: Variables complexes [math.CV]; Géométrie algébrique [math.AG]

Mats Andersson, Hakan Samuelsson, Elizabeth Wulcan, Alain Yger. Segre numbers, a generalized King formula , and local intersections. 2015. ⟨hal-01026124⟩