| 概要 | The pioneering papers of Griffiths and Fulton and Lazarsfeld
investigated numerical positivity related to ample vector
bundles in differential and algebraic geometry.
Their various variants are nowadays widely investigated
in algebraic geometry. Among main objects of global
singularity theory are the Thom polynomials of singularity
classes. We shall consider Thom polynomials of singularities
of mappings and Lagrangian and Legendrian Thom polynomials.
We shall show that in some bases coming from representation
theory, they admit positive expansions. These can be applied
to upper bounds of their coefficients. An open problem on
positivity of Morin singularities seems to be connected
with the Green-Griffiths conjecture. |