Topic
Todd class
About: Todd class is a research topic. Over the lifetime, 528 publications have been published within this topic receiving 11638 citations.
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1 / 2
Papers
Book•
1 Jan 1966
TL;DR: In this paper, the Riemann-Roch theorem for algebraic manifolds and complex analytic vector bundles is presented. But the authors do not consider the complexity of complex analytic line bundles.
Abstract: Introduction Chapter 1: Preparatory material 1. Multiplicative sequences 2. Sheaves 3. Fibre bundles 4. Characteristic classes Chapter 2: The cobordism ring 5. Pontrjagin numbers 6. The ring /ss(/Omega) /oplus //Varrho 7. The cobordism ring /omega 8. The index of a 4k-dimensional manifold 9. The virtual index Chapter 3: The Todd genus 10. Definiton of the Todd genus 11. The virutal generalised Todd genus 12. The t-characteristic of a GL(q, C)-bundle 13. Split manifolds and splitting methods 14. Multiplicative properties of the Todd genus Chapter 4: The Riemann-Roch theorem for algebraic manifolds 15. Cohomology of Compact complex manifolds 16. Further properties of the (/chi)x characteristics 17. The virtual (/chi)x characteristics 18. Some fundamental theorems of Kodaira 19. The virtual (/chi)x characteristics for algebraic manifolds 20. The Riemann-Roch theorem for algebraic manifolds and complex analytic line bundles 21. The Riemann-Roch theorem for algebraic manifolds and complex analytic vector bundles Appendix 1 by R.L.E. Schwarzenberger 22. Applications of the Riemann-Roch theorem 23. The Riemann-Roch theorem of Grothendieck 24. The Grothendieck ring of continuous vector bundles 25. The Atijah-Singer index theorem 26. Integrality theorems for differentiable manifolds Appendix 2 by A. Borel A spectral sequence for complex analytic bundles Bibliography Index
1,577 citations
700 citations
1 Jan 1987
TL;DR: Theorem 1.1 as discussed by the authors deals with a sort of inequality for the first and second Chern classes of normal projective varieties with numerically effective canonical classes (1.1); to some extent it is a continuation of the author's previous paper [Mil] in which the surface case was discussed.
Abstract: This paper deals with a sort of inequality for the first and second Chern classes of normal projective varieties with numerically effective canonical classes (Theorem 1.1); to some extent it is a continuation of the author's previous paper [Mil] in which the surface case was discussed. Our generalized inequality will be, however, farther-reaching in connexion with the classification theory of algebraic varieties developed by S. Iitaka, K. Ueno, M. Reid, E. Viehweg, S. Mori, Y. Kawamata and many others. For instance, we can derive the non-negativity of the Kodaira dimension for certain "minimal" threefolds (Theorem 1.2), which is a crucial step in the classification of threefolds after the construction of minimal models of non-uniruled varieties (the so-called "minimal model conjecture", see (6.5) below). The precise statements of our results are as follows:
528 citations
TL;DR: The operational Chow cohomology classes of a complete toric variety are identified with certain functions, called Minkowski weights, on the corresponding fan as discussed by the authors, and the natural product of these functions makes the Minkowowski weights into a commutative ring; the product is computed by a displacement in the lattice, which corresponds to a deformation in the toric manifold.
286 citations
TL;DR: In this article, the Chern classes of tautological bundles on the cohomology of Hilbert schemes of points on surfaces were studied in the framework of Nakajima's oscillator algebra.
Abstract: We give an algorithmic description of the action of the Chern classes of tautological bundles on the cohomology of Hilbert schemes of points on surfaces within the framework of Nakajima's oscillator algebra. This leads to an identification of the cohomology ring of Hilbert schemes of the affine plane with a ring of differential operators on a Fock space. We end with the computation of the top Segre classes of tautological bundles associated to line bundles on Hilb^n up to n=7, and give a conjecture for the generating series.
259 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 3 |
| 2019 | 5 |
| 2018 | 3 |
| 2017 | 8 |
| 2016 | 19 |
| 2015 | 16 |