Perturbed Dolbeault operators and the homology Todd class
HTML articles powered by AMS MathViewer
- by Jeffrey Fox and Peter Haskell PDF
- Proc. Amer. Math. Soc. 128 (2000), 3715-3721 Request permission
Abstract:
This paper discusses the role played by perturbed Dolbeault operators in relating the coherent sheaf and elliptic operator perspectives on the $K$ homology of projective varieties. Among the consequences are index formulas for perturbed Dolbeault operators.References
- Saad Baaj and Pierre Julg, Théorie bivariante de Kasparov et opérateurs non bornés dans les $C^{\ast }$-modules hilbertiens, C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), no. 21, 875–878 (French, with English summary). MR 715325
- Paul Baum, Riemann-Roch theorem for singular varieties, Differential geometry (Proc. Sympos. Pure Math., Vol. XXVII, Stanford Univ., Stanford, Calif., 1973) Amer. Math. Soc., Providence, R.I., 1975, pp. 3–16. MR 0389907
- Paul Baum, William Fulton, and Robert MacPherson, Riemann-Roch for singular varieties, Inst. Hautes Études Sci. Publ. Math. 45 (1975), 101–145. MR 412190, DOI 10.1007/BF02684299
- N. V. Borisov and K. N. Ilinski, $N=2$ supersymmetric quantum mechanics on Riemann surfaces with meromorphic superpotentials, Comm. Math. Phys. 161 (1994), no. 1, 177–194. MR 1266074, DOI 10.1007/BF02099417
- Sylvain E. Cappell and Julius L. Shaneson, Stratifiable maps and topological invariants, J. Amer. Math. Soc. 4 (1991), no. 3, 521–551. MR 1102578, DOI 10.1090/S0894-0347-1991-1102578-4
- Maurizio Cornalba and Phillip Griffiths, Analytic cycles and vector bundles on non-compact algebraic varieties, Invent. Math. 28 (1975), 1–106. MR 367263, DOI 10.1007/BF01389905
- William Fulton and Serge Lang, Riemann-Roch algebra, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 277, Springer-Verlag, New York, 1985. MR 801033, DOI 10.1007/978-1-4757-1858-4
- J. Fox, C. Gajdzinski, and P. Haskell, Homology Chern characters of perturbed Dirac operators, Houston J. Math., to appear.
- J. Fox and P. Haskell, Index theory of perturbed Dolbeault operators: smooth polar divisors, Internat. J. Math., to appear.
- R. Hartshorne, Algebraic Geometry, Springer-Verlag, New York, 1977.
- Heisuke Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II, Ann. of Math. (2) 79 (1964), 109–203; ibid. (2) 79 (1964), 205–326. MR 0199184, DOI 10.2307/1970547
- Sławomir Klimek and Andrzej Lesniewski, Local rings of singularities and $N=2$ supersymmetric quantum mechanics, Comm. Math. Phys. 136 (1991), no. 2, 327–344. MR 1096119, DOI 10.1007/BF02100028
- Dan Kucerovsky, The $KK$-product of unbounded modules, $K$-Theory 11 (1997), no. 1, 17–34. MR 1435704, DOI 10.1023/A:1007751017966
- I. R. Porteous, Blowing up Chern classes, Proc. Cambridge Philos. Soc. 56 (1960), 118–124. MR 121813, DOI 10.1017/s0305004100034368
- Mark Stern, Index theory for certain complete Kähler manifolds, J. Differential Geom. 37 (1993), no. 3, 467–503. MR 1217157
Additional Information
- Jeffrey Fox
- Affiliation: Department of Mathematics, University of Colorado, Boulder, Colorado 80309
- Email: jfox@euclid.colorado.edu
- Peter Haskell
- Affiliation: Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
- Email: haskell@math.vt.edu
- Received by editor(s): February 4, 1999
- Published electronically: June 7, 2000
- Additional Notes: The first author’s work was supported by the National Science Foundation.
The second author’s work was supported by the National Science Foundation under Grant No. DMS-9800782. - Communicated by: Jozef Dodziuk
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 3715-3721
- MSC (2000): Primary 58J20, 19L10, 19K35
- DOI: https://doi.org/10.1090/S0002-9939-00-05488-5
- MathSciNet review: 1695143