In this paper we prove a result on the effective generation of pluri-canonical linear systems on foliated surfaces of general type. Fix a function , then there exists an integer such that if is a canonical or nef model of a foliation of general type with Hilbert polynomial for all , then defines a birational map for all .
On the way, we also prove a Grauert–Riemenschneider-type vanishing theorem for foliated surfaces with canonical singularities.
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The first author was partially supported by NSF, research grants no. DMS-1801851, DMS-1840190,
and by a grant from the Simons foundation, award number 256202.
The second author was partially supported by Narodowe Centrum Nauki, contract number 2018/29/B/ST1/01232.
Journal für die reine und angewandte Mathematik is the oldest mathematics periodical still in existence. Founded in 1826 by August Leopold Crelle and edited by him until his death in 1855, it soon became widely known under the name of
Crelle’s Journal. In the 190 years of its existence,
Crelle’s Journal has developed to an outstanding scholarly periodical with one of the worldwide largest circulations among mathematics journals.