JournalsjemsVol. 14, No. 4pp. 1081–1101

Algebraic cobordism of bundles on varieties

  • Rahul Pandharipande

    ETH Zürich, Switzerland
  • Y.-P. Lee

    University of Utah, Salt Lake City, United States
Algebraic cobordism of bundles on varieties cover
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Abstract

The double point relation defines a natural theory of algebraic cobordism for bundles on varieties. We construct a simple basis (over Q\mathbb Q) of the corresponding cobordism groups over Spec(C)\text{Spec}(\mathbb C) for all dimensions of varieties and ranks of bundles. The basis consists of split bundles over products of projective spaces. Moreover, we prove the full theory for bundles on varieties is an extension of scalars of standard algebraic cobordism.

Cite this article

Rahul Pandharipande, Y.-P. Lee, Algebraic cobordism of bundles on varieties. J. Eur. Math. Soc. 14 (2012), no. 4, pp. 1081–1101

DOI 10.4171/JEMS/327