64 research outputs found
Positivity of Schur function expansions of Thom polynomials
Combining the Kazarian approach to Thom polynomials via classifying spaces of
singularities with the Fulton-Lazarsfeld theory of numerical positivity for
ample vector bundles, we show that the coefficients of various Schur function
expansions of the Thom polynomials of stable and unstable singularities are
nonnegative.Comment: 12 pages, various modification of the expositio
Positivity of Thom polynomials II: the Lagrange singularities
We show that Thom polynomials of Lagrangian singularities have nonnegative
coefficients in the basis consisting of Q-functions. The main tool in the proof
is nonnegativity of cone classes for globally generated bundles.Comment: 16 pages, reduced introduction but new chapter about Legendrian
singularities. The title is change. Correction in the formula for A_7 and a
sign correction in formula (29
Thom polynomials and Schur functions: the singularities I_{2,2}(-)
We give the Thom polynomials for the singularities associated with
maps with parameter . Our computations combine the characterization of Thom polynomials via the
``method of restriction equations'' of Rimanyi et al. with the techniques of
Schur functions.Comment: 21 pages; Ann. Inst. Fourier vol.57; this is expanded Sect.4 of
math.AG/0509234; new added results: Theorem 11 (based on P-ideals of
singularities) and explicit expressions for the coefficients of the Thom
polynomials of I_22(-) (Propositions 17, 18, 19); references update
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