Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On the zero set of a holomorphic one-form on a compact complex manifold
HTML articles powered by AMS MathViewer

by Michael J. Spurr PDF
Trans. Amer. Math. Soc. 308 (1988), 329-339 Request permission

Abstract:

On any compact complex surface $M$, divisors of nonnegative self-intersection which are contained in the zero set (or in the integral set) of a holomorphic $1$-form are shown to induce a fibration of $M$ onto a Riemann surface. This result is extended to higher dimensions for $M$ projective. Applications to zero sets of holomorphic $1$-forms on surfaces are given.
References
  • Enrico Bombieri and Dale Husemoller, Classification and embeddings of surfaces, Algebraic geometry (Proc. Sympos. Pure Math., Vol. 29, Humboldt State Univ., Arcata, Calif., 1974) Amer. Math. Soc., Providence, R.I., 1975, pp. 329–420. MR 0506292
  • James B. Carrell and David I. Lieberman, Holomorphic vector fields and Kaehler manifolds, Invent. Math. 21 (1973), 303–309. MR 326010, DOI 10.1007/BF01418791
  • F. Catanese, On the moduli spaces of surfaces of general type, J. Differential Geom. 19 (1984), no. 2, 483–515. MR 755236
  • Hans Grauert, Über Modifikationen und exzeptionelle analytische Mengen, Math. Ann. 146 (1962), 331–368 (German). MR 137127, DOI 10.1007/BF01441136
  • K. Kodaira, On the structure of compact complex analytic surfaces. I, Amer. J. Math. 86 (1964), 751–798. MR 187255, DOI 10.2307/2373157
  • C. P. Ramanujam, Remarks on the Kodaira vanishing theorem, J. Indian Math. Soc. (N.S.) 36 (1972), 41–51. MR 330164
  • Andrew John Sommese, On the density of ratios of Chern numbers of algebraic surfaces, Math. Ann. 268 (1984), no. 2, 207–221. MR 744608, DOI 10.1007/BF01456086
    • M. J. Spurr, On the zero set of a holomorphic one-form, Thesis, Tulane Univ., 1983.
  • M. J. Spurr, On the genus of an irreducible component of the zero set of a holomorphic one-form, Topics in several complex variables (Mexico, 1983) Res. Notes in Math., vol. 112, Pitman, Boston, MA, 1985, pp. 158–163. MR 805601
  • Kenji Ueno, Classification theory of algebraic varieties and compact complex spaces, Lecture Notes in Mathematics, Vol. 439, Springer-Verlag, Berlin-New York, 1975. Notes written in collaboration with P. Cherenack. MR 0506253
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 32J15, 32L10, 32L99
  • Retrieve articles in all journals with MSC: 32J15, 32L10, 32L99
Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 308 (1988), 329-339
  • MSC: Primary 32J15; Secondary 32L10, 32L99
  • DOI: https://doi.org/10.1090/S0002-9947-1988-0946446-3
  • MathSciNet review: 946446