@article{ASENS_1988_4_21_3_413_0, author = {Pragacz, Piotr}, title = {Enumerative geometry of degeneracy loci}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {413--454}, publisher = {Elsevier}, volume = {Ser. 4, 21}, number = {3}, year = {1988}, doi = {10.24033/asens.1563}, mrnumber = {90e:14004}, zbl = {0687.14043}, language = {en}, url = {https://www.numdam.org/articles/10.24033/asens.1563/} }
TY - JOUR AU - Pragacz, Piotr TI - Enumerative geometry of degeneracy loci JO - Annales scientifiques de l'École Normale Supérieure PY - 1988 SP - 413 EP - 454 VL - 21 IS - 3 PB - Elsevier UR - https://www.numdam.org/articles/10.24033/asens.1563/ DO - 10.24033/asens.1563 LA - en ID - ASENS_1988_4_21_3_413_0 ER -
Pragacz, Piotr. Enumerative geometry of degeneracy loci. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 21 (1988) no. 3, pp. 413-454. doi : 10.24033/asens.1563. https://www.numdam.org/articles/10.24033/asens.1563/
[B-R] Hook Young Diagrams With Applications to Combinatorics and to Representation Theory of Lie Superalgebras (Adv. in Math., Vol. 64, pp. 118-175, 1987). | MR | Zbl
, ,[B-H] Pieri Formula for SO2n + 1/Un and Spn/Un (Adv. in Math., Vol. 62, pp. 49-68, 1986). | MR | Zbl
, ,[F] Intersection Theory, Springer Verlag, 1984. | MR | Zbl
,[G-G] Stable Mappings and their Singularities (Graduate Texts in Math., Vol. 14, Springer-Verlag, 1973). | MR | Zbl
, ,[H-T] Chern Numbers of Kernel and Cokernel Bundles (Invent. Math., Vol. 75, pp. 467-475, 1984). | MR | Zbl
, ,[H] Topological Methods in Algebraic Geometry (Grundlehren der Math., Wissenschaften, Vol. 131, 1956, Third Enlarged, Springer-Verlag, 1966). | MR | Zbl
,[J-L-P] Classes of Determinantal Varieties Associated with Symmetric and Antisymmetric Matrices (Izwiestja A.N. S.S.S.R., Vol. 45, N° 9, pp. 662-673, 1981). | MR | Zbl
, , ,[K-L] The Determinantal Formula of Schubert Calculus (Acta Math., Vol. 132, pp. 153-162, 1974). | MR | Zbl
, ,[L-L-T] On Giambelli's Theorem on Complete Correlations, to Appear in Acta Mathematica. | Zbl
, , ,[L] Puissances extérieures, déterminants et cycles de Schubert (Bull. Soc. Math., France, Vol. 102, pp. 161-179, 1974). | Numdam | MR | Zbl
,[L-S] Formulaire raisonné de fonctions symétriques, prépublication de l'Université Paris VII, 1985.
, ,[M] Symmetric Functions and Hall Polynomials, Oxford Univ. Press, 1979. | MR | Zbl
,[Mo] A Note on the Multiplication of Hall Functions (J. London Math. Soc., Vol. 39, pp. 481-488, 1964). | MR | Zbl
,[Po] Simple Singularities of Maps, Proc. Liverpool Singularities Symposium I (Lecture Notes in Mathematics, Vol. 192, pp. 286-307, 1971). | MR | Zbl
,[P1] Determinantal Varieties and Symmetric Polynomials (Functional Analysis and Its Applications, Vol. 21, N° 3, pp. 89-90, 1987). | MR | Zbl
,[P2] A Note on Elimination Theory (Proc. Kon. Ned. Akad. van Wetensh., Vol. A 90 (2) (= Indagationes Math., Vol. 49 (2)), pp. 215-221, 1987). | MR | Zbl
,[P3] Algebro-Geometric Applications of Schur S- and Q-Polynomials (in preparation in Séminaire d'Algèbre Dubreil-Malliavin 1987-1988, Springer Lecture Notes in Math.). | Zbl
,[S] Allgemaine Anzahlfunctionen für Kegelschnitte, Flöchen und Röume zweiten Grades in n Dimensionen (Math. Ann., Vol. 45, pp. 153-206, 1894). | JFM
,[Sch] Uber die Darstellung der Symmetrischen und den Alternierenden Gruppe durch Gebrochene Lineare Substitutionen (Journal für die reine u. angew. Math., Vol. 139, pp. 155-250, 1911). | JFM
,[St] Problem 4 in Problem Session, Combinatorics and Algebra (Contemporary Mathematics, A.M.S., Vol. 34, 1984). | MR
,[T] Les ensembles singuliers d'une application différentiable et leurs propriétés homologiques, Séminaire de Topologie de Strasbourg, (December 1957).
,- Initial values of ML-degree polynomials, Advances in Applied Mathematics, Volume 164 (2025), p. 102831 | DOI:10.1016/j.aam.2024.102831
- A raising operator formula for Macdonald polynomials, Forum of Mathematics, Sigma, Volume 13 (2025) | DOI:10.1017/fms.2025.8
- Gysin formulas and equivariant cohomology, Group Actions and Equivariant Cohomology, Volume 808 (2024), p. 235 | DOI:10.1090/conm/808/16188
- On the Hessian of Cubic Hypersurfaces, International Mathematics Research Notices, Volume 2024 (2024) no. 10, p. 8672 | DOI:10.1093/imrn/rnad324
- On some invariants of cubic fourfolds, European Journal of Mathematics, Volume 9 (2023) no. 3 | DOI:10.1007/s40879-023-00651-y
- Hilbert squares of degeneracy loci, Rendiconti del Circolo Matematico di Palermo Series 2, Volume 72 (2023) no. 6, p. 3153 | DOI:10.1007/s12215-022-00832-w
- Neutral-fermionic presentation of the K-theoretic Q-function, Journal of Algebraic Combinatorics, Volume 55 (2022) no. 2, p. 629 | DOI:10.1007/s10801-021-01064-4
- The Strong Maximal Rank conjecture and higher rank Brill–Noether theory, Journal of the London Mathematical Society, Volume 104 (2021) no. 1, p. 169 | DOI:10.1112/jlms.12427
- Integrable models and K-theoretic pushforward of Grothendieck classes, Nuclear Physics B, Volume 971 (2021), p. 115513 | DOI:10.1016/j.nuclphysb.2021.115513
- K-theoretic Chern class formulas for vexillary degeneracy loci, Advances in Mathematics, Volume 350 (2019), p. 440 | DOI:10.1016/j.aim.2019.04.049
- Universal Gysin formulas for flag bundles, International Journal of Mathematics, Volume 28 (2017) no. 11, p. 1750077 | DOI:10.1142/s0129167x1750077x
- Dual pairs of gauged linear sigma models and derived equivalences of Calabi–Yau threefolds, Journal of Geometry and Physics, Volume 114 (2017), p. 223 | DOI:10.1016/j.geomphys.2016.12.005
- Two-dimensional gauge dynamics and the topology of singular determinantal varieties, Journal of High Energy Physics, Volume 2017 (2017) no. 3 | DOI:10.1007/jhep03(2017)132
- A Gysin formula for Hall-Littlewood polynomials, Proceedings of the American Mathematical Society, Volume 143 (2015) no. 11, p. 4705 | DOI:10.1090/s0002-9939-2015-12623-8
- Lines on some Calabi–Yau threefolds in
P 4, Rendiconti del Circolo Matematico di Palermo (1952 -), Volume 63 (2014) no. 3, p. 457 | DOI:10.1007/s12215-014-0167-5 - A Giambelli formula for classical 𝐺/𝑃 spaces, Journal of Algebraic Geometry, Volume 23 (2013) no. 2, p. 245 | DOI:10.1090/s1056-3911-2013-00604-9
- Thom series of contact singularities, Annals of Mathematics, Volume 176 (2012) no. 3, p. 1381 | DOI:10.4007/annals.2012.176.3.1
- The algebraic degree of semidefinite programming, Mathematical Programming, Volume 122 (2010) no. 2, p. 379 | DOI:10.1007/s10107-008-0253-6
- Skew-symmetric matrices and Palatini scrolls, Mathematische Annalen, Volume 347 (2010) no. 4, p. 859 | DOI:10.1007/s00208-009-0450-5
- Thom Polynomials of Invariant Cones, Schur Functions and Positivity, Algebraic Cycles, Sheaves, Shtukas, and Moduli (2008), p. 117 | DOI:10.1007/978-3-7643-8537-8_7
- Examples of Calabi–Yau Threefolds as Covers of Almost-Fano Threefolds, Geometriae Dedicata, Volume 119 (2006) no. 1, p. 169 | DOI:10.1007/s10711-006-9067-y
- Degeneracy of 2-Forms and 3-Forms, Canadian Mathematical Bulletin, Volume 48 (2005) no. 4, p. 547 | DOI:10.4153/cmb-2005-050-9
- Low degree 3‐folds in P6, Mathematische Nachrichten, Volume 278 (2005) no. 1-2, p. 17 | DOI:10.1002/mana.200310223
- Combinatorial K-theory, Topics in Cohomological Studies of Algebraic Varieties (2005), p. 87 | DOI:10.1007/3-7643-7342-3_3
- A Littlewood-Richardson rule for the K-theory of Grassmannians, Acta Mathematica, Volume 189 (2002) no. 1, p. 37 | DOI:10.1007/bf02392644
- Common subbundles and intersections of divisors, Algebraic Geometric Topology, Volume 2 (2002) no. 2, p. 1061 | DOI:10.2140/agt.2002.2.1061
- Grothendieck classes of quiver varieties, Duke Mathematical Journal, Volume 115 (2002) no. 1 | DOI:10.1215/s0012-7094-02-11513-0
- Schur Q-Functions and Degeneracy Locus Formulas for Morphisms with Symmetries, Recent Progress in Intersection Theory (2000), p. 239 | DOI:10.1007/978-1-4612-1316-1_8
- A Generalization of the Macdonald–You Formula, Journal of Algebra, Volume 204 (1998) no. 2, p. 573 | DOI:10.1006/jabr.1997.7342
- On topological Radon transformations, Journal of Pure and Applied Algebra, Volume 120 (1997) no. 3, p. 235 | DOI:10.1016/s0022-4049(96)00047-3
- Determinantal formulas for orthogonal and symplectic degeneracy loci, Journal of Differential Geometry, Volume 43 (1996) no. 2 | DOI:10.4310/jdg/1214458108
- Chern-Schwartz-MacPherson classes and the Euler characteristic of degeneracy loci and special divisors, Journal of the American Mathematical Society, Volume 8 (1995) no. 4, p. 793 | DOI:10.1090/s0894-0347-1995-1311826-0
- On the class of Brill-Noether loci for Prym varieties, Mathematische Annalen, Volume 302 (1995) no. 1, p. 687 | DOI:10.1007/bf01444512
- Gröbner bases and multiplicity of determinantal and pfaffian ideals, Advances in Mathematics, Volume 96 (1992) no. 1, p. 1 | DOI:10.1016/0001-8708(92)90050-u
- On schur’s Q-functions, Communications in Algebra, Volume 19 (1991) no. 9, p. 2429 | DOI:10.1080/00927879108824271
- Algebro — Geometric applications of schur s- and q-polynomials, Topics in Invariant Theory, Volume 1478 (1991), p. 130 | DOI:10.1007/bfb0083503
- On Giambelli's theorem on complete correlations, Acta Mathematica, Volume 162 (1989) no. 0, p. 143 | DOI:10.1007/bf02392836
Cité par 37 documents. Sources : Crossref