scholarly journals Boundary expression for Chern classes of the Hodge bundle on spaces of cyclic covers

2021 ◽  
Vol 14 (4) ◽  
pp. 571-594
Author(s):  
Bryson Owens ◽  
Seamus Somerstep ◽  
Renzo Cavalieri
Keyword(s):  
Chern Classes ◽  
Cyclic Covers

scholarly journals Tensors with eigenvectors in a given subspace

2021 ◽  
Author(s):  
Giorgio Ottaviani ◽  
Zahra Shahidi
Keyword(s):  
Algebraic Geometry ◽  
Linear Subspace ◽  
Chern Classes ◽  
Symmetric Tensors

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.

scholarly journals Topology of Subvarieties of Complex Semi-abelian Varieties

2020 ◽  
Author(s):  
Yongqiang Liu ◽  
Laurentiu Maxim ◽  
Botong Wang
Keyword(s):  
Euler Characteristic ◽  
Morse Theory ◽  
Characteristic Property ◽  
Abelian Varieties ◽  
Betti Numbers ◽  
Local Systems ◽  
Affine Manifolds ◽  
Cyclic Covers ◽  
Rank One ◽  
Generic Vanishing

Abstract We use the non-proper Morse theory of Palais–Smale to investigate the topology of smooth closed subvarieties of complex semi-abelian varieties and that of their infinite cyclic covers. As main applications, we obtain the finite generation (except in the middle degree) of the corresponding integral Alexander modules as well as the signed Euler characteristic property and generic vanishing for rank-one local systems on such subvarieties. Furthermore, we give a more conceptual (topological) interpretation of the signed Euler characteristic property in terms of vanishing of Novikov homology. As a byproduct, we prove a generic vanishing result for the $L^2$-Betti numbers of very affine manifolds. Our methods also recast June Huh’s extension of Varchenko’s conjecture to very affine manifolds and provide a generalization of this result in the context of smooth closed sub-varieties of semi-abelian varieties.

scholarly journals A remark on branched cyclic covers

1993 ◽  
Vol 87 (3) ◽  
pp. 237-240
Author(s):  
Jonathan A. Hillman
Keyword(s):  
Cyclic Covers ◽  
Branched Cyclic Covers

scholarly journals A Construction of Chern Classes of Parabolic Vector Bundles

2013 ◽  
Vol 42 (3) ◽  
pp. 1111-1122 ◽  
Author(s):  
Indranil Biswas ◽  
Ajneet Dhillon
Keyword(s):  
Vector Bundles ◽  
Chern Classes

IWASAWA TYPE FORMULA FOR COVERS OF A LINK IN A RATIONAL HOMOLOGY SPHERE

2008 ◽  
Vol 17 (10) ◽  
pp. 1199-1221 ◽  
Author(s):  
TERUHISA KADOKAMI ◽  
YASUSHI MIZUSAWA
Keyword(s):  
Number Field ◽  
Class Number ◽  
Homology Sphere ◽  
Rational Homology ◽  
Homology Groups ◽  
Cyclic Covers ◽  
Class Number Formula ◽  
Number Formula ◽  
Iwasawa Invariants ◽  
Rational Homology Sphere

Based on the analogy between links and primes, we present an analogue of the Iwasawa's class number formula in a Zp-extension for the p-homology groups of pn-fold cyclic covers of a link in a rational homology 3-sphere. We also describe the associated Iwasawa invariants precisely for some examples and discuss analogies with the number field case.

scholarly journals Chern classes of tensor products

2016 ◽  
Vol 27 (10) ◽  
pp. 1650079 ◽  
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.

scholarly journals Transfers of Chern classes in BP-cohomology and Chow rings

2000 ◽  
Vol 353 (3) ◽  
pp. 1039-1054 ◽  
Author(s):  
Björn Schuster ◽  
Nobuaki Yagita
Keyword(s):  
Chern Classes ◽  
Chow Rings
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