Higher Todd Classes and Holomorphic Group Actions

Block, Jonathan; Weinberger, Shmuel

doi:10.4310/pamq.2006.v2.n4.a13

Cited by 9 publications

(13 citation statements)

References 36 publications

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“…There are a few reasons for this. First of all, the appearance of [4] and of [5] confirms that our Conjecture 1.2 seems to be of interest. Second, the results of section 4 appear to be new and of independent interest.…”

Section: Introduction and Statement Of The Conjecturesupporting

confidence: 73%

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An analogue of the Novikov Conjecture in complex algebraic geometry

Rosenberg

2008

Trans. Amer. Math. Soc.

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Abstract. We introduce an analogue of the Novikov Conjecture on higher signatures in the context of the algebraic geometry of (nonsingular) complex projective varieties. This conjecture asserts that certain "higher Todd genera" are birational invariants. This implies birational invariance of certain extra combinations of Chern classes (beyond just the classical Todd genus) in the case of varieties with large fundamental group (in the topological sense). We prove the conjecture under the assumption of the "strong Novikov Conjecture" for the fundamental group, which is known to be correct for many groups of geometric interest. We also show that, in a certain sense, our conjecture is best possible.

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Section: Introduction and Statement Of The Conjecturesupporting

confidence: 73%

“…A similar argument can be found in [4], which points out that the results of [3] can be used to prove the corresponding fact in K-homology, that under the same hypotheses,…”

Section: Introduction and Statement Of The Conjecturesupporting

confidence: 61%

An analogue of the Novikov Conjecture in complex algebraic geometry

Rosenberg

2008

Trans. Amer. Math. Soc.

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“…The work [26] conjectures that in the case when X is projective algebraic and nonsingular the higher Todd invariants (T d(X) ∪ f * (α))[X], where T d is the total Todd class, are birational invariants. The work [3] contains a proof of this conjecture but also raises the problem of generalizing it to higher elliptic genera. The purpose of this note is to present such a generalization for the (two-variable) elliptic genus.…”

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confidence: 99%

Higher elliptic genera

Borisov¹,

Libgober

2008

Mathematical Research Letters

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We show that elliptic classes introduced in [7] for spaces with infinite fundamental groups yield Novikov's type higher elliptic genera which are invariants of K-equivalence. This include, as a special case, the birational invariance of higher Todd classes studied recently by J.Rosenberg and J.Block-S.Weinberger. We also prove the modular properties of these genera, show that they satisfy a McKay correspondence, and consider their twist by discrete torsion.

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“…without assuming the rational injectivity of β. See [3] and also [6] for a more analytic approach. These articles use in a crucial way the weak factorization theorem for birational maps, [1].…”

Section: Introductionmentioning

confidence: 99%

A note on higher Todd genera of complex manifolds

Bei,

Piazza

2020

Preprint

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Higher Todd Classes and Holomorphic Group Actions

Cited by 9 publications

References 36 publications

An analogue of the Novikov Conjecture in complex algebraic geometry

An analogue of the Novikov Conjecture in complex algebraic geometry

Higher elliptic genera

A note on higher Todd genera of complex manifolds

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