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Demailly's Conjecture and the containment problem
Affiliation:1. Tulane University, Department of Mathematics, 6823 St. Charles Ave., New Orleans, LA 70118, USA;2. Department of Mathematics, University of Nebraska – Lincoln, Lincoln, NE 68588, USA;3. University of Education, Hue University, 34 Le Loi St., Hue, Viet Nam;1. Key Laboratory of Mathematical Theory and Computation in Information Security, School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, PR China;2. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, PR China;1. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland;2. Mathematical Institute, Oxford University, ROQ, Oxford OX2 6GG, United Kingdom;3. Institute of Engineering, Tokyo University of Agriculture and Technology, Nakacho 2-24-16, Koganei, Tokyo 184-8588, Japan
Abstract:We investigate Demailly's Conjecture for a general set of sufficiently many points. Demailly's Conjecture generalizes Chudnovsky's Conjecture in providing a lower bound for the Waldschmidt constant of a set of points in projective space. We also study a containment between symbolic and ordinary powers conjectured by Harbourne and Huneke that in particular implies Demailly's bound, and prove that a general version of this containment holds for generic determinantal ideals and defining ideals of star configurations.
Keywords:Chudnovsky's Conjecture  Waldschmidt constant  Ideals of points  Symbolic powers  Containment problem  Stable Harbourne–Huneke Conjecture
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