منابع مشابه
Positivity of Legendrian Thom polynomials
We study Legendrian singularities arising in complex contact geometry. We define a one-parameter family of bases in the ring of Legendrian characteristic classes such that any Legendrian Thom polynomial has nonnegative coefficients when expanded in these bases. The method uses a suitable Lagrange Grassmann bundle on the product of projective spaces. This is an extension of a nonnegativity resul...
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Combining the approach to Thom polynomials via classifying spaces of singularities with the Fulton-Lazarsfeld theory of cone classes and positive polynomials for ample vector bundles, we show that the coefficients of the Schur function expansions of the Thom polynomials of stable singularities are nonnegative with positive sum.
متن کاملThom polynomials of invariant cones , Schur functions , and positivity
We generalize the notion of Thom polynomials from singularities of maps between two complex manifolds to invariant cones in representations, and collections of vector bundles. We prove that the generalized Thom polynomials, expanded in the products of Schur functions of the bundles, have nonnegative coefficients. For classical Thom polynomials associated with maps of complex manifolds, this giv...
متن کاملThom Polynomials of Morin Singularities
We begin with a quick summary of the notions of global singularity theory and the theory of Thom polynomials. For a more detailed review we refer the reader to [1, 15]. Let N and K be two complex manifolds of dimensions n and k respectively; assume that n ≤ k. Consider a holomorphic map f : N → K for which the differential d fp : TpN → TpK at a generic point p ∈ N is nonsingular, i.e. has rank ...
متن کامل6 S ep 2 00 9 Positivity of Thom polynomials II : the Lagrange singularities
We study Thom polynomials associated with Lagrange singularities. We expand them in the basis of Q̃-functions. This basis plays a key role in the Schubert calculus of isotropic Grassmannians. We prove that the Q̃-function expansions of Thom polynomials of Lagrange singularities have always nonnegative coefficients. This is an analog of a result on Thom polynomials of mapping singularities and Sch...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 2011
ISSN: 0022-040X
DOI: 10.4310/jdg/1324476753