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Linear series have long played a central role in algebraic geometry. In recent years, starting with seminal papers by Demailly and Ein-Lazarsfeld, local properties of linear series – in particular local positivity, as measured by Seshadri constants – have come into focus. Interestingly, in their multi-point version they are closely related to the famous Nagata conjecture on plane curves. While a number of important basic results are available by now, there are still a large number of open questions and even completely open lines of research.
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Thomas Bauer, Sandra Di Rocco, Brian Harbourne, Tomasz Szemberg, Mini-Workshop: Linear Series on Algebraic Varieties. Oberwolfach Rep. 7 (2010), no. 4, pp. 2613–2650DOI 10.4171/OWR/2010/45