Title: Bounds on Seshadri Constants on Surfaces with Picard Number 1
Abstract: Abstract In this note we improve a result of Steffens [7 Steffens , A. ( 1998 ). Remarks on Seshadri constants . Math. Z. 227 : 505 – 510 .[Crossref], [Web of Science ®] , [Google Scholar]] on the lower bound for Seshadri constants in very general points of a surface with 1-dimensional Néron–Severi space. We also show a multi-point counterpart of such a lower bound. Key Words: Nagata conjectureSeshadri constant2010 AMS Subject Classification: 14C20 ACKNOWLEDGMENTS This work was partially supported by a MNiSW grant N N201 388834. I would like to thank the Max Planck Institute für Mathematik in Bonn, where this work has began, for warm hospitality, and Thomas Bauer for interesting discussions. I would like also to thank the referee for helpful remarks.