Skip to main content
SpringerLink
Log in

Curvature of determinant bundles for degenerate families

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

We calculate the (1, 1) curvature of the Beilinson Schechtman connection for the determinant bundle associated to a family of Riemann surfaces with ordinary singularities. As consequences we obtain generalizations of theorems of Bismut and Bost.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • [BS] Beilinson, A., Schechtman, V.: Determinant bundles and Virasoro algebras. Commun. Math. Phys.118, 651–701 (1988)

    Google Scholar 

  • [BB] Bismut, J.M., Bost, J.B.: Fibrés déterminants, métriques de Quillen et dégénérescence des courbes. Acta. Math.165 1–103 (1990)

    Google Scholar 

  • [D] Deligne, P.: Le déterminant de la cohomologie. Contemporary Mathematics, vol.67, 93–178

  • [Mum] Mumford, D.: The red book of varieties and schemes. Lecture Notes in Math. V.1358, Berlin, Heidelberg, New York: Springer 1988

    Google Scholar 

  • [T] Tong, Yue Lin L.: Connections on determinant bundles. J. Alg. Geom., 443–486 (1993)

  • [TTs] Tong, Yue Lin L., Tsai, I-Hsun: An identification of the connections of Quillen and Beilinson-Schechtman. Commun. Math. Phys.159, 443–457 (1994)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Purdue University, 47907, West Lafayette, IN, USA

    Yue Lin L. Tong

  2. National Taiwan University, Taipei, Taiwan, Republic of China

    I-Hsun Tsai

Authors
  1. Yue Lin L. Tong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I-Hsun Tsai
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by S.-T. Yau

Supported in part by NSF Grant No DMS-9201022.

Supported in part by NSC Grant No 83-0208-M-002-039, Republic of China.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tong, Y.L.L., Tsai, IH. Curvature of determinant bundles for degenerate families. Commun.Math. Phys. 171, 589–606 (1995). https://doi.org/10.1007/BF02104679

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02104679

Keywords

Search

Navigation