The dimension of the moduli space of superminimal surfaces of a fixed degree and conformal structure in the 4-sphere

Authors
Citation
Qs. Chi, The dimension of the moduli space of superminimal surfaces of a fixed degree and conformal structure in the 4-sphere, TOHOKU MATH, 52(2), 2000, pp. 299-308
Citations number
11
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematics
Journal title
TOHOKU MATHEMATICAL JOURNAL
ISSN journal
0040-8735 → ACNP
Volume
52
Issue
2
Year of publication
2000
Pages
299 - 308
Database
ISI
SICI code
0040-8735(200006)52:2<299:TDOTMS>2.0.ZU;2-O
Abstract
It was established by X. Mo and the author that the dimension of each irred ucible component of the moduli space M-d,M-g(X) of branched superminimal im mersions of degree d from a Riemann surface X of genus g into CP3 lay betwe en 2d-4g+4 and 2d-g+4 ford sufficiently large, where the upper bound was al ways assumed by the irreducible component of totally geodesic branched supe rminimal immersions and the lower bound was assumed by all nontotally geode sic irreducible components of M-6,M-1(T) for any torus T. It is shown, via deformation theory, in this note that for d = 89 + 1 + 3k, k greater than o r equal to 0, and any Riemann surface X of g greater than or equal to 1, th e above lower bound is assumed by at least one irreducible component of Md, g(X).