Elliptic operators and a theorem of Poincaré
Elliptic operators and a theorem of Poincaré
A general vanishing theorem is proved for elliptic operators. This result is then used to give a simple proof of the fact that the arithmetic genus vanishes for complex manifolds of odd dimension <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n"> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding="application/x-tex">n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with nowhere zero <inline-formula content-type="math/mathml"> …