Segre classes of monomial schemes
نویسندگان
چکیده
منابع مشابه
Segre Classes of Monomial Schemes
We propose an explicit formula for the Segre classes of monomial subschemes of nonsingular varieties, such as schemes defined by monomial ideals in projective space. The Segre class is expressed as a formal integral on a region bounded by the corresponding Newton polyhedron. We prove this formula for monomial ideals in two variables and verify it for some families of examples in any number of v...
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We prove a closed formula for the integrals of the top Segre classes of tautological bundles over the Hilbert schemes of points of a K3 surface X. We derive relations among the Segre classes via equivariant localization of the virtual fundamental classes of Quot schemes on X. The resulting recursions are then solved explicitly. The formula proves the K-trivial case of a conjecture of M. Lehn fr...
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We study a class obtained from the Segre class s(Z, Y ) of an embedding of schemes by incorporating the datum of a line bundle on Z. This class satisfies basic properties analogous to the ordinary Segre class, but leads to remarkably simple formulas in standard intersection-theoretic situations such as excess or residual intersections. We prove a formula for the behavior of this class under lin...
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We propose a variation of the notion of Segre class, by forcing a naive `inclusion-exclusion' principle to hold. The resulting class is computationally tractable, and is closely related to Chern-Schwartz-MacPherson classes. We deduce several general properties of the new class from this relation, and obtain an expression for the Milnor class of an arbitrary scheme in terms of this class.
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This article studies jet schemes of monomial schemes. They are known to be equidimensional but usually are not reduced [13]. We thus investigate their structure further, giving a formula for the multiplicity along every component of the jet schemes of a general reduced monomial hypersurface (that is, the case of a simple normal crossing divisor).
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ژورنال
عنوان ژورنال: Electronic Research Announcements in Mathematical Sciences
سال: 2013
ISSN: 1935-9179
DOI: 10.3934/era.2013.20.55