Open Access
September 2011 Positivity of Legendrian Thom polynomials
Małgorzata Mikosz, Piotr Pragacz, Andrzej Weber
J. Differential Geom. 89(1): 111-132 (September 2011). DOI: 10.4310/jdg/1324476753


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 non- negativity result for Lagrangian Thom polynomials obtained by the authors previously. For a fixed specialization, other special- izations of the parameter lead to upper bounds for the coefficients of the given basis. One gets also upper bounds of the coefficients from the positivity of classical Thom polynomials (of singularities of mappings), obtained previously by the last two authors.


Download Citation

Małgorzata Mikosz. Piotr Pragacz. Andrzej Weber. "Positivity of Legendrian Thom polynomials." J. Differential Geom. 89 (1) 111 - 132, September 2011.


Published: September 2011
First available in Project Euclid: 21 December 2011

zbMATH: 1238.05275
MathSciNet: MR2863914
Digital Object Identifier: 10.4310/jdg/1324476753

Rights: Copyright © 2011 Lehigh University

Vol.89 • No. 1 • September 2011
Back to Top