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1
Content available remote

Leray residue for singular varieties

100%
Weber A.
Banach Center Publications
|
1998
|
tom 44
|
nr 1
247-256
2
Content available remote

Weights in the cohomology of toric varieties

100%
Weber A.
Open Mathematics
|
2004
|
tom 2
|
nr 3
478-492
EN
We describe the weight filtration in the cohomology of toric varieties. We present a role of the Frobenius automorphism in an elementary way. We prove that equivariant intersection homology of an arbitrary toric variety is pure. We obtain results concerning Koszul duality: nonequivariant intersection cohomology is equal to the cohomology of the Koszul complexIH T*(X)⊗H*(T). We also describe the weight filtration inIH *(X).
3
Content available remote

Positivity of Schur function expansions of Thom polynomials

63%
Pragacz P., Weber A.
Fundamenta Mathematicae
|
2007
|
tom 195
|
nr 1
85-95
EN
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.
4
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Positivity of Thom polynomials II: the Lagrange singularities

51%
Mikosz M., Pragacz P., Weber A.
Fundamenta Mathematicae
|
2009
|
tom 202
|
nr 1
65-79
EN
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 the Thom polynomials of Lagrange singularities always have nonnegative coefficients. This is an analog of a result on the Thom polynomials of mapping singularities and Schur S-functions, established formerly by the last two authors.
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