## Hermitian vector bundles and value distribution for Schubert cycles

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- by Michael J. Cowen PDF
- Trans. Amer. Math. Soc.
**180**(1973), 189-228 Request permission

## Abstract:

R. Bott and S. S. Chern used the theory of characteristic differential forms of a holomorphic hermitian vector bundle to study the distribution of zeroes of a holomorphic section. In this paper their methods are extended to study how often a holomorphic mapping into a Grassmann manifold hits Schubert cycles of fixed type.## References

- Thomas Bloom and Miguel Herrera,
*De Rham cohomology of an analytic space*, Invent. Math.**7**(1969), 275–296. MR**248349**, DOI 10.1007/BF01425536 - Raoul Bott and S. S. Chern,
*Hermitian vector bundles and the equidistribution of the zeroes of their holomorphic sections*, Acta Math.**114**(1965), 71–112. MR**185607**, DOI 10.1007/BF02391818 - S. S. Chern,
*Complex manifolds without potential theory*, Van Nostrand Mathematical Studies, No. 15, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR**0225346** - Herbert Federer,
*Geometric measure theory*, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York, Inc., New York, 1969. MR**0257325** - Harley Flanders,
*Differential forms with applications to the physical sciences*, Academic Press, New York-London, 1963. MR**0162198** - Phillip A. Griffiths,
*Hermitian differential geometry, Chern classes, and positive vector bundles*, Global Analysis (Papers in Honor of K. Kodaira), Univ. Tokyo Press, Tokyo, 1969, pp. 185–251. MR**0258070** - 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 - John J. Hirschfelder,
*The first main theorem of value distribution in several variables*, Invent. Math.**8**(1969), 1–33. MR**245840**, DOI 10.1007/BF01418868 - W. V. D. Hodge and D. Pedoe,
*Methods of algebraic geometry. Vol. II. Book III: General theory of algebraic varieties in projective space. Book IV: Quadrics and Grassmann varieties*, Cambridge, at the University Press, 1952. MR**0048065** - James R. King,
*The currents defined by analytic varieties*, Acta Math.**127**(1971), no. 3-4, 185–220. MR**393550**, DOI 10.1007/BF02392053 - Pierre Lelong,
*Intégration sur un ensemble analytique complexe*, Bull. Soc. Math. France**85**(1957), 239–262 (French). MR**95967**, DOI 10.24033/bsmf.1488 - Wilhelm Stoll,
*Value distribution of holomorphic maps into compact complex manifolds.*, Lecture Notes in Mathematics, Vol. 135, Springer-Verlag, Berlin-New York, 1970. MR**0267138**, DOI 10.1007/BFb0059118 - Gabriel Stolzenberg,
*Volumes, limits, and extensions of analytic varieties*, Lecture Notes in Mathematics, No. 19, Springer-Verlag, Berlin-New York, 1966. MR**0206337**, DOI 10.1007/BFb0097736 - H. Wu,
*Remarks on the first main theorem in equidistribution theory. I*, J. Differential Geometry**2**(1968), 197–202. MR**276500**

## Additional Information

- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**180**(1973), 189-228 - MSC: Primary 32H25
- DOI: https://doi.org/10.1090/S0002-9947-1973-0333252-5
- MathSciNet review: 0333252