ar X iv : a lg - g eo m / 9 60 20 19 v 1 2 7 Fe b 19 96 FORMULAS FOR LAGRANGIAN AND ORTHOGONAL DEGENERACY LOCI ; The Q̃ - Polynomials Approach
نویسندگان
چکیده
Introduction 1. Schubert subschemes and their desingularizations. 2. Isotropic Schubert calculus and the class of the diagonal. 3. Subbundles intersecting an n-subbundle in dim > k. 4. Q̃-polynomials and their properties. 5. Divided differences and isotropic Gysin maps; orthogonality of Q̃-polynomials. 6. Single Schubert condition. 7. Two Schubert conditions. 8. An operator proof of Proposition 3.1. 9. Main results in the generic case. Appendix A: Quaternionic Schubert calculus. Appendix B: Introduction to Schubert polynomials à la polonaise. References
منابع مشابه
ar X iv : a st ro - p h / 96 01 16 3 v 1 2 9 Ja n 19 96 Lagrangian Dynamics of Collisionless Matter
The non–linear dynamics of self–gravitating irrotational dust is analyzed in a general relativistic framework, using synchronous and comoving coordinates. Writing the equations in terms of the metric tensor of the spatial sections orthogonal to the fluid flow allows an unambiguous expansion in inverse powers of the speed of light. The Newtonian and post–Newtonian approximations are derived in L...
متن کاملQuantum Cohomology of Orthogonal Grassmannians
Let V be a vector space with a nondegenerate symmetric form and OG be the orthogonal Grassmannian which parametrizes maximal isotropic subspaces in V . We give a presentation for the (small) quantum cohomology ring QH∗(OG) and show that its product structure is determined by the ring of P̃ -polynomials. A ‘quantum Schubert calculus’ is formulated, which includes quantum Pieri and Giambelli formu...
متن کاملar X iv : m at h - ph / 0 30 40 46 v 1 2 9 A pr 2 00 3 Symmetries and Hamiltonian formalism for complex materials
Preliminary results toward the analysis of the Hamiltonian structure of multifield theories describing complex materials are mustered: we involve the invariance under the action of a general Lie group of the balance of substructural interactions. Poisson brackets are also introduced in the material representation to account for general material substructures. A Hamilton-Jacobi equation suitable...
متن کاملar X iv : m at h . A G / 9 90 61 71 v 1 2 5 Ju n 19 99 ENRIQUES SURFACES AND OTHER NON
We give examples of subcanonical subvarieties of codimension 3 in projective n-space which are not Pfaffian, i.e. defined by the ideal sheaf of submaximal Pfaffians of an alternating map of vector bundles. This gives a negative answer to a question asked by Okonek [29]. Walter [36] had previously shown that a very large majority of subcanonical subschemes of codimension 3 in P are Pfaffian, but...
متن کاملFe b 20 09 CLASSICAL INTEGRABLE FIELD THEORIES IN DISCRETE 2 + 1 DIMENSIONAL SPACE - TIME
We study “circular net” (discrete orthogonal net) equations for angular data generalized by external spectral parameters. A criterion defining physical regimes of these Hamiltonian equations is the reality of Lagrangian density. There are four distinct regimes for fields and spectral parameters classified by four types of spherical or hyperbolic triangles. Non-zero external spectral parameters ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1996