Integral Hodge classes on fourfolds fibered by quadric bundles

Zhiyuan Li; Zhiyu Tian

doi:10.1090/proc/12999

Integral Hodge classes on fourfolds fibered by quadric bundles

Proceedings of the American Mathematical Society ◽

10.1090/proc/12999 ◽

2016 ◽

Vol 144 (8) ◽

pp. 3333-3345

Author(s):

Zhiyuan Li ◽

Zhiyu Tian

Keyword(s):

Quadric Bundles

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Motives of quadric bundles

manuscripta mathematica ◽

10.1007/s00229-015-0783-1 ◽

2015 ◽

Vol 149 (3-4) ◽

pp. 347-368 ◽

Cited By ~ 3

Author(s):

Johann Bouali

Keyword(s):

Quadric Bundles

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TOPOLOGY OF QUADRIC BUNDLES

International Journal of Mathematics ◽

10.1142/s0129167x01001167 ◽

2001 ◽

Vol 12 (09) ◽

pp. 1005-1047 ◽

Cited By ~ 1

Author(s):

YOGISH I. HOLLA ◽

NITIN NITSURE

Keyword(s):

Quadric Bundles

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Chern class formulas for classical-type degeneracy loci

Compositio Mathematica ◽

10.1112/s0010437x18007224 ◽

2018 ◽

Vol 154 (8) ◽

pp. 1746-1774 ◽

Cited By ~ 3

Author(s):

David Anderson ◽

William Fulton

Keyword(s):

Large Class ◽

Chern Class ◽

Geometric Approach ◽

Classical Type ◽

Degeneracy Loci ◽

Basic Formula ◽

The Subject ◽

Quadric Bundles

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.

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