Euler classes and complete intersections

S Mandal, R Sridharan - Journal of Mathematics of Kyoto …, 1996 - projecteuclid.org
S Mandal, R Sridharan
Journal of Mathematics of Kyoto University, 1996projecteuclid.org
Theorem 1. Let A be a reduced affine algebra of dimension n over an algebraically closed
field F with F" K o (A) torsion free. Suppose P is a projective A-module of rank n. Let f: P—> I
be a surjection where I g A is a local complete intersection of height n. Assume that [A/I]= 0 in
K o (A). Then there exists a surjection from P to A.(ie If the top Chern class of P vanishes,
then P has a unimodular element.)
Theorem 1. Let A be a reduced affine algebra of dimension n over an algebraically closed field F with F" K o (A) torsion free. Suppose P is a projective A-module of rank n. Let f: P—> I be a surjection where I g A is a local complete intersection of height n. Assume that [A/I]= 0 in K o (A). Then there exists a surjection from P to A.(ie If the top Chern class of P vanishes, then P has a unimodular element.)
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