Kodaira dimension and symplectic sums

• Autores: Michael Usher
• Localización: Commentarii mathematici helvetici, ISSN 0010-2571, Vol. 84, Nº 1, 2009, págs. 57-85
• Idioma: inglés
• DOI: 10.4171/cmh/152
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• Resumen

  • Modulo trivial exceptions, we show that symplectic sums of symplectic 4-manifolds along surfaces of positive genus are never rational or ruled, and we enumerate each case in which they have Kodaira dimension zero (i.e., are blowups of symplectic 4-manifolds with torsion canonical class). In particular, a symplectic four-manifold of Kodaira dimension zero arises by such a surgery only if it is diffeomorphic to a blowup either of the K3 surface, the Enriques surface, or a member of a particular family of T2-bundles over T2 each having b1 = 2.