Thom polynomials and Schur functions : the singularities A 3 ( − )
نویسندگان
چکیده
Combining the “method of restriction equations” of Rimányi et al. with the techniques of symmetric functions, we establish the Schur function expansions of the Thom polynomials for the Morin singularities A3 : (C •, 0) → (C, 0) for any nonnegative integer k.
منابع مشابه
Thom polynomials and Schur functions I
We give the Thom polynomials for the singularities I2,2, and A3 associated with maps (C•, 0) → (C, 0) with parameter k ≥ 0. We give the Schur function expansions of these Thom polynomials. Moreover, for the singularities Ai (with any parameter k ≥ 0) we analyze the “first approximation” F (i) to the Thom polynomial. Our computations combine the characterization of Thom polynomials via the “meth...
متن کاملThom Polynomials and Schur Functions: the Singularities a 3 (−) to the Memory of Stanis Law Balcerzyk
Combining the “method of restriction equations” of Rimányi et al. with the techniques of symmetric functions, we establish the Schur function expansions of the Thom polynomials for the Morin singularities A3 : (C •, 0) → (C, 0) for any nonnegative integer k.
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 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...
متن کاملPositivity of Schur function expansions of Thom polynomials
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008