New York Journal of Mathematics
Volume 28 (2022), 1172-1192


Josef G. Dorfmeister

Minimal genus and simplified classes in rational manifolds

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Published: August 22, 2022.
Keywords: Minimal Genus, Rational Manifolds, 4-Manifolds, Geometric Automorphism Group, Lorentz Orthogonal Transformation, Quadratic Forms.
Subject [2010]: 57R40, 57N35, 57R95, 57R50.

This note studies the minimal genus problem for classes which are equivalent, via the geometric diffeomorphism group, to a simplified class in CP2#kCP2. It is shown that the orbit structure for primitive classes is basically determined by the self-intersection number. Making use of this result, an upper bound for the minimal genus for each orbit is determined and it is shown that for k large enough, then genus stabilizes at either 0 or 1.


The author would like to thank Tian-Jun Li for useful suggestions to improve this paper.

Author information

Josef G. Dorfmeister:
Department of Mathematics
North Dakota State University
Fargo, ND 58102, USA