Symbolic Powers of Ideals

  • Hailong Dao
  • Alessandro De Stefani
  • Eloísa Grifo
  • Craig Huneke
  • Luis Núñez-Betancourt
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 222)

Abstract

We survey classical and recent results on symbolic powers of ideals. We focus on properties and problems of symbolic powers over regular rings, on the comparison of symbolic and regular powers, and on the combinatorics of the symbolic powers of monomial ideals. In addition, we present some new results on these aspects of the subject.

Keywords

Symbolic powers Differential operators Uniform Symbolic Topologies Packing problem 

Notes

Acknowledgements

We thank Jeff Mermin for many helpful conversations concerning the packing problem, and in particular for discussions leading to Remark 4.19 and Corollary 4.20. We thank Jonathan Montaño, Andrew Conner, Jack Jeffries, and Robert Walker for helpful comments. Part of this work was done when the second and fifth authors were at the University of Virginia. They wish to thank this institution for its hospitality. Finally, the fifth author thanks the organizing committee for the ‘Brazil-Mexico 2nd meeting on Singularities’ in Salvador, Bahia, Brazil, where this project was initiated.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Hailong Dao
    • 1
  • Alessandro De Stefani
    • 2
  • Eloísa Grifo
    • 3
  • Craig Huneke
    • 3
  • Luis Núñez-Betancourt
    • 4
  1. 1.Department of MathematicsUniversity of KansasLawrenceUSA
  2. 2.Department of MathematicsUniversity of NebraskaLincolnUSA
  3. 3.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA
  4. 4.Centro de Investigación en MatemáticasGuanajuatoMexico

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