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Deligne pairing and determinant bundle
1. | School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India |
2. | Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Lahnberge, Hans-Meerwein-Strasse, D-35032 Marburg, Germany |
3. | Graduate School of Mathematics, Kyushu University Fukuoka, 819-0395, Japan |
References:
[1] |
J.-M. Bismut, H. Gillet and C. Soulé, Analytic torsion and holomorphic determinant bundles. I: Bott-Chern forms and analytic torsion, Commun. Math. Phys., 115 (1988), 49-78.
doi: 10.1007/BF01238853. |
[2] |
P. Deligne, "Le Déterminant de la Cohomologie," Current Trends in Arithmetical Algebraic Geometry, 93-177, Contemp. Math. 67, Amer. Math. Soc., Providence, RI, 1987. |
[3] |
R. Elkik, Métriques sur les fibrés d'intersection, Duke Math. Jour., 61 (1990), 303-328.
doi: 10.1215/S0012-7094-90-06113-7. |
[4] |
J. Franke, Chow categories, Algebraic Geometry (Berlin, 1988), Compositio Math., 76 (1990), 101-162. |
[5] |
C. Gasbarri, Heights and geometric invariant theory, Forum Math., 12 (2000), 135-153.
doi: 10.1515/form.2000.001. |
[6] |
A. Fujiki and G. Schumacher, The moduli space of extremal compact Kähler manifolds and generalized Weil-Petersson metrics, Publ. Res. Inst. Math. Sci., 26 (1990), 101-183.
doi: 10.2977/prims/1195171664. |
[7] |
F. Knudsen and D. Mumford, The projectivity of the moduli space of stable curves. I: Preliminaries on "det" and "Div," Math. Scand., 39 (1976), 19-55. |
[8] |
S. Kobayashi, "Differential Geometry of Complex Vector Bundles," Publications of the Mathematical Society of Japan, 15, Kanô Memorial Lectures, 5, Princeton University Press, Princeton, NJ, Iwanami Shoten, Tokyo, 1987. |
[9] |
T. Mabuchi and L. Weng, Kähler-Einstein metrics and Chow-Mumford stability, preprint, 1998. |
[10] |
D. H. Phong and J. Sturm, Scalar curvature, moment maps, and the Deligne pairing, Amer. Jour. Math., 126 (2004), 693-712.
doi: 10.1353/ajm.2004.0019. |
[11] |
D. H. Phong, J. Ross and J. Sturm, Deligne pairings and the Knudsen-Mumford expansion, Jour. Diff. Geom., 78 (2008), 475-496. |
[12] |
D. G. Quillen, Determinants of Cauchy-Riemann operators on Riemann surfaces, (Russian), Funktsional. Anal. i Prilozhen, 19 (1985), 37-41. |
[13] |
S. Zhang, Heights and reductions of semi-stable varieties, Compos. Math., 104 (1996), 77-105. |
show all references
References:
[1] |
J.-M. Bismut, H. Gillet and C. Soulé, Analytic torsion and holomorphic determinant bundles. I: Bott-Chern forms and analytic torsion, Commun. Math. Phys., 115 (1988), 49-78.
doi: 10.1007/BF01238853. |
[2] |
P. Deligne, "Le Déterminant de la Cohomologie," Current Trends in Arithmetical Algebraic Geometry, 93-177, Contemp. Math. 67, Amer. Math. Soc., Providence, RI, 1987. |
[3] |
R. Elkik, Métriques sur les fibrés d'intersection, Duke Math. Jour., 61 (1990), 303-328.
doi: 10.1215/S0012-7094-90-06113-7. |
[4] |
J. Franke, Chow categories, Algebraic Geometry (Berlin, 1988), Compositio Math., 76 (1990), 101-162. |
[5] |
C. Gasbarri, Heights and geometric invariant theory, Forum Math., 12 (2000), 135-153.
doi: 10.1515/form.2000.001. |
[6] |
A. Fujiki and G. Schumacher, The moduli space of extremal compact Kähler manifolds and generalized Weil-Petersson metrics, Publ. Res. Inst. Math. Sci., 26 (1990), 101-183.
doi: 10.2977/prims/1195171664. |
[7] |
F. Knudsen and D. Mumford, The projectivity of the moduli space of stable curves. I: Preliminaries on "det" and "Div," Math. Scand., 39 (1976), 19-55. |
[8] |
S. Kobayashi, "Differential Geometry of Complex Vector Bundles," Publications of the Mathematical Society of Japan, 15, Kanô Memorial Lectures, 5, Princeton University Press, Princeton, NJ, Iwanami Shoten, Tokyo, 1987. |
[9] |
T. Mabuchi and L. Weng, Kähler-Einstein metrics and Chow-Mumford stability, preprint, 1998. |
[10] |
D. H. Phong and J. Sturm, Scalar curvature, moment maps, and the Deligne pairing, Amer. Jour. Math., 126 (2004), 693-712.
doi: 10.1353/ajm.2004.0019. |
[11] |
D. H. Phong, J. Ross and J. Sturm, Deligne pairings and the Knudsen-Mumford expansion, Jour. Diff. Geom., 78 (2008), 475-496. |
[12] |
D. G. Quillen, Determinants of Cauchy-Riemann operators on Riemann surfaces, (Russian), Funktsional. Anal. i Prilozhen, 19 (1985), 37-41. |
[13] |
S. Zhang, Heights and reductions of semi-stable varieties, Compos. Math., 104 (1996), 77-105. |
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