Open Access
July, 2001 On reducible hyperplane sections of 4-folds
Antonio LANTERI, Andrea L. TIRONI
J. Math. Soc. Japan 53(3): 559-563 (July, 2001). DOI: 10.2969/jmsj/05330559


We describe 4-dimensional complex projective manifolds X admitting a simple normal crossing divisor of the form A+B among their hyperplane sections, both components A and B having sectional genus zero. Let L be the hyperplane bundle. Up to exchanging the two components, (X,L,A,B) is one of the following: 1)(X,L) is a scroll over P1 with A itself a scroll and B a fibre, 2)(X,L)=(P2×P2,OP2×P2(1,1)) with A|OP2×P2(1,0)|,B|OP2×P2(0,1)|,3)X=PP2(V) where V=OP2(1)2OP2(2), L is the tautological line bundle, A=PP2 (OP2(1)2, and Bπ*|OP2(2)| , where π : XP2 is the scroll projection. This supplements a recent result of Chandler, Howard, and Sommese.


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Antonio LANTERI. Andrea L. TIRONI. "On reducible hyperplane sections of 4-folds." J. Math. Soc. Japan 53 (3) 559 - 563, July, 2001.


Published: July, 2001
First available in Project Euclid: 9 June 2008

zbMATH: 1076.14503
MathSciNet: MR1828969
Digital Object Identifier: 10.2969/jmsj/05330559

Primary: 14J35
Secondary: 14C20 , 14J45 , 14N30

Keywords: 4-folds , adjunction theory , Fano manifolds , hyperplane sections , Simple normal crossing divisors

Rights: Copyright © 2001 Mathematical Society of Japan

Vol.53 • No. 3 • July, 2001
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