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pro vyhledávání: '"Pragacz A"'
In this note, we study the behaviour of the Lojasiewicz exponent under hyperplane sections and its relation to the order of tangency.
Comment: 8 pages; v3 improves the exposition of the proof of Theorem 2 and gives a new Observation 4 on the ord
Comment: 8 pages; v3 improves the exposition of the proof of Theorem 2 and gives a new Observation 4 on the ord
Externí odkaz:
http://arxiv.org/abs/2003.13031
We study the order of tangency between two manifolds of same dimension and give that notion three quite different geometric interpretations. Related aspects of the order of tangency, e.g., regular separation exponents, are also discussed.
Commen
Commen
Externí odkaz:
http://arxiv.org/abs/1803.07664
Autor:
Darondeau, Lionel, Pragacz, Piotr
In this note, we give Gysin formulas for partial flag bundles for the classical groups. We then give Gysin formulas for Schubert varieties in Grassmann bundles, including isotropic ones. All these formulas are proved in a rather uniform way by using
Externí odkaz:
http://arxiv.org/abs/1802.09039
Autor:
Pragacz, Piotr
We report on results of Kra\'skiewicz and the author, and Watanabe on KP modules materializing Schubert polynomials, and filtrations having KP modules as their subquotients. We discuss applications of KP filtrations and ample KP bundles to positivity
Externí odkaz:
http://arxiv.org/abs/1603.00189
Autor:
Darondeau, Lionel, Pragacz, Piotr
Publikováno v:
Fundamenta Mathematicae 244 (2019), 191-208
We establish a Gysin formula for Schubert bundles and a strong version of the duality theorem in Schubert calculus on Grassmann bundles. We then combine them to compute the fundamental classes of Schubert bundles in Grassmann bundles, which yields a
Externí odkaz:
http://arxiv.org/abs/1602.01983
Publikováno v:
Comptes Rendus. Mathématique, Vol 359, Iss 8, Pp 991-997 (2021)
In this note, we investigate the behaviour of the Łojasiewicz exponent under hyperplane sections and its relation to the order of tangency.
Externí odkaz:
https://doaj.org/article/21b2210614054b63b9577c934741e555
Autor:
Darondeau, Lionel, Pragacz, Piotr
We give push-forward formulas for all flag bundles of types A, B, C, D. The formulas (and also the proofs) involve only Segre classes of the original vector bundles and characteristic classes of universal bundles. As an application, we provide new de
Externí odkaz:
http://arxiv.org/abs/1510.07852
Autor:
Kaji, Shizuo, Pragacz, Piotr
We express the diagonals of projective, Grassmann and, more generally, flag bundles of type (A) using the zero schemes of some vector bundle sections, and do the same for their single point subschemes. We discuss diagonal and point properties of thes
Externí odkaz:
http://arxiv.org/abs/1503.03217
Autor:
Pragacz, Piotr
Publikováno v:
Proc. Amer. Math. Soc. 143 (2015) no.11, 4705-4711
We give a formula for pushing forward the classes of Hall-Littlewood polynomials in Grassmann bundles, generalizing Gysin formulas for Schur S- and Q-functions.
Comment: 7 pages; the version corresponding to the published one and its corrigenda,
Comment: 7 pages; the version corresponding to the published one and its corrigenda,
Externí odkaz:
http://arxiv.org/abs/1403.0788
Autor:
Pragacz, Piotr
Publikováno v:
Advances Studies in Pure Mathematics 71, 2016, Schubert calculus - Osaka 2012, pp. 419-451
We describe the positivity of Thom polynomials of singularities of maps, Lagrangian Thom polynomials and Legendrian Thom polynomials. We show that these positivities come from Schubert calculus.
Comment: 27 pages; v4: final version
Comment: 27 pages; v4: final version
Externí odkaz:
http://arxiv.org/abs/1304.2573