Segre numbers, a generalized King formula, and local intersections

• Let $\mathcal{J}$ 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–Ampère products $(dd^c \log |f|^2)^k$, where $f$ is a tuple of generators of $\mathcal{J}$, coincide with theso-called Segre numbers of $\mathcal{J}$, introduced independently by Tworzewski, Achilles–Manaresi,and Gaffney–Gassler. More generally we show that these currents satisfy a generalization ofthe classical King formula that takes into account fixed and moving components of Vogelcycles associated with $\mathcal{J}$. A basic tool is a new calculus for products of positive currents ofBochner–Martinelli type. We also discuss connections to intersection theory.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Geometri (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Geometry (hsv//eng)

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

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