Poincaré Bundle and Chern Classes

AbstractThe first author with B. Sturmfels studied in [16] the variety of matrices with eigenvectors in a given linear subspace, called the Kalman variety. We extend that study from matrices to symmetric tensors, proving in the tensor setting the irreducibility of the Kalman variety and computing its codimension and degree. Furthermore, we consider the Kalman variety of tensors having singular t-tuples with the first component in a given linear subspace and we prove analogous results, which are new even in the case of matrices. Main techniques come from Algebraic Geometry, using Chern classes for enumerative computations.

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A Residue Formula for Chern Classes Associated with Logarithmic Connections

Tokyo Journal of Mathematics ◽

10.3836/tjm/1270215030 ◽

1982 ◽

Vol 05 (1) ◽

pp. 13-21 ◽

Cited By ~ 11

Author(s):

Makoto OHTSUKI

Keyword(s):

Chern Classes ◽

Residue Formula

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A Construction of Chern Classes of Parabolic Vector Bundles

Communications in Algebra ◽

10.1080/00927872.2012.732639 ◽

2013 ◽

Vol 42 (3) ◽

pp. 1111-1122 ◽

Cited By ~ 1

Author(s):

Indranil Biswas ◽

Ajneet Dhillon

Keyword(s):

Vector Bundles ◽

Chern Classes

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Chern classes of tensor products

International Journal of Mathematics ◽

10.1142/s0129167x16500798 ◽

2016 ◽

Vol 27 (10) ◽

pp. 1650079 ◽

Cited By ~ 2

Author(s):

Laurent Manivel

Keyword(s):

Vector Bundles ◽

Tensor Products ◽

Chern Classes ◽

Explicit Formulas

We prove explicit formulas for Chern classes of tensor products of virtual vector bundles, whose coefficients are given by certain universal polynomials in the ranks of the two bundles.

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