Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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



On the zero set of a holomorphic one-form on a compact complex manifold

Author: Michael J. Spurr
Journal: Trans. Amer. Math. Soc. 308 (1988), 329-339
MSC: Primary 32J15; Secondary 32L10, 32L99
MathSciNet review: 946446
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] E. Bombieri and D. Husemoller, Classification and embeddings of surfaces, Proc. Sympos. Pure Math., vol. 29, Amer. Math., Soc., Providence, R.I., 1975, pp. 329-420. MR 0506292 (58:22085)
  • [2] J. B. Carrell and D. I. Lieberman, Holomorphic vector fields and compact Kaehler manifolds, Invent. Math. 21 (1973), 303-309. MR 0326010 (48:4356)
  • [3] F. Catanese, On the moduli spaces of surfaces of general type, J. Differential Geom. 19 (1984), 483-515. MR 755236 (86h:14031)
  • [4] H. Grauert, Über Modifikationen und exzeptionelle analytische Menger, Math. Ann. 146 (1962) 331-368. MR 0137127 (25:583)
  • [5] K. Kodaira, On the structure of compact complex surfaces. I, Amer. J. Math. 86 (1964), 751-798. MR 0187255 (32:4708)
  • [6] C. P. Ramanujam, Remarks on the Kodaira vanishing theorem, J. Indian Math. Soc. 36 (1972), 41-51. MR 0330164 (48:8502)
  • [7] A. J. Sommese, On the density of ratios of Chern numbers of algebraic surfaces, Math. Ann. 268 (1984), 207-221. MR 744608 (86d:14037)
  • [8] M. J. Spurr, On the zero set of a holomorphic one-form, Thesis, Tulane Univ., 1983.
  • [9] -, On the genus of an irreducible component of the zero set of a holomorphic one-form, Topics in Several Complex Variables, Research Notes in Math., vol. 112, Pitman Press, 1985. MR 805601 (87m:32063)
  • [10] K. Ueno, Classification theory of algebraic varieties and compact complex spaces, Lecture Notes in Math., vol. 439, Springer-Verlag, Berlin and New York, 1975. MR 0506253 (58:22062)

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

Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society