Chern class formulas for classical-type degeneracy loci
Chern class formulas for classical-type degeneracy loci
复制标题
经典型简并位点的陈氏类公式
作者：
David Anderson;W. Fulton
采用一个简单而直接的几何方法，我们证明了一个大类的退化轨迹类型B，C和D，包括那些来自所有各向同性格拉斯曼公式。所得结果统一和推广了以前的Pfronian公式和行列式公式。专门的格拉斯曼的情况下，我们恢复显着的布赫，Kresch，Tamvakis和威尔逊的θ-和eta-多项式。我们的方法产生精简的证明，并行进行的所有四个经典类型，大大简化了以前的工作。在附录中，我们发展了一些基础代数，并证明了几个Pfweian恒等式。另一个附录建立了二次丛中类的基本公式。
Employing a simple and direct geometric approach, we prove formulas for a large class of degeneracy loci in types B, C, and D, including those coming from all isotropic Grassmannians. The results unify and generalize previous Pfaffian and determinantal formulas. Specializing to the Grassmannian case, we recover the remarkable theta- and eta-polynomials of Buch, Kresch, Tamvakis, and Wilson. Our method yields streamlined proofs which proceed in parallel for all four classical types, substantially simplifying previous work on the subject. In an appendix, we develop some foundational algebra and prove several Pfaffian identities. Another appendix establishes a basic formula for classes in quadric bundles.