On the zero set of a holomorphic oneform

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Title 
On the zero set of a holomorphic oneform 
Author 
Spurr, Michael Jerome 
School 
Tulane University 
Academic Field 
Mathematics 
Abstract 
The zero set of a holomorphic 1form (phi) on a compact complex surface S is studied. The main result gives, under the assumption that (phi) has a onedimensional zero set with appropriate selfintersection properties, the existence of a holomorphic map f : S (>) R onto a Riemann surface. The form (phi) is a pullback via f of a holomorphic 1form on R and the zero set of (phi) is contained in fibers of f. As a direct consequence of this, any divisor D having the same support as D(,(phi)), the divisor associated to (phi), is shown to satisfy D(.)D (LESSTHEQ) 0 In a different direction, the genus of an irreducible component of the zero set of a holomorphic 1form is proved to be bounded in terms of the Euler number of S. It is also shown that all curves having sufficiently low genus and zero selfintersection must be contained in the zero set of some holomorphic 1form on S A structure theorem for elliptic surfaces having a nonvanishing holomorphic 1form is proved and examples are provided 
Language 
eng 
Degree Date 
1983 
Degree 
Ph.D 
Publisher 
Tulane University 
Publication Date 
1983 
Source 
91 p., Dissertation Abstracts International, Volume: 4409, Section: B, page: 2781 
Identifier 
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Rights 
Copyright is in accordance with U.S. Copyright law 
Contact Information 
acase@tulane.edu 
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