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On the projective normality of cyclic coverings over a rational surface
Author(s) -
Song Lei
Publication year - 2019
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms.12247
Subject(s) - mathematics , divisor (algebraic geometry) , normality , surface (topology) , rational surface , integer (computer science) , projective test , pure mathematics , combinatorics , discrete mathematics , geometry , statistics , physics , plasma , quantum mechanics , computer science , programming language
Let S be a rational surface withdim | − K S | ⩾ 1and let π : X → S be a ramified cyclic covering from a nonruled smooth surface X . We show that for any integer k ⩾ 3 and ample divisor A on S , the adjoint divisorK X + k π ∗ A is very ample and normally generated. Similar result holds for minimal (possibly singular) coverings.