@article{Nagata1959,
  author = {Nagata, Masayoshi},
  title = {On the 14-th Problem of {Hilbert}},
  journal = {American Journal of Mathematics},
  volume = {81},
  pages = {766--772},
  year = {1959},
  doi = {10.2307/2372927},
  url = {https://doi.org/10.2307/2372927}
}

@book{Nagata1965,
  author = {Nagata, Masayoshi},
  title = {Lectures on the Fourteenth Problem of {Hilbert}},
  series = {Tata Institute of Fundamental Research Lectures on Mathematics},
  volume = {31},
  publisher = {Tata Institute of Fundamental Research},
  address = {Bombay},
  year = {1965},
  note = {Notes by M. Pavaman Murthy},
  url = {https://mathweb.tifr.res.in/Documents/Publications/Lectures/tifr31.pdf}
}

@article{Roe2001,
  author = {Ro{\'e}, Joaquim},
  title = {On the existence of plane curves with imposed multiple points},
  journal = {Journal of Pure and Applied Algebra},
  volume = {156},
  number = {1},
  pages = {115--126},
  year = {2001},
  doi = {10.1016/S0022-4049(99)00116-4},
  eprint = {math/9807066v2},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://arxiv.org/abs/math/9807066v2}
}

@article{Harbourne2001,
  author = {Harbourne, Brian},
  title = {On {Nagata}'s conjecture},
  journal = {Journal of Algebra},
  volume = {236},
  number = {2},
  pages = {692--702},
  year = {2001},
  doi = {10.1006/jabr.2000.8515},
  eprint = {math/9909093},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://doi.org/10.1006/jabr.2000.8515}
}

@article{CMR2026,
  author = {Ciliberto, Ciro and Miranda, Rick and Ro{\'e}, Joaquim},
  title = {Irrational Nef Rays at the Boundary of the {Mori} Cone for Very General Blowups of the Plane},
  journal = {Michigan Mathematical Journal},
  volume = {76},
  pages = {143--161},
  year = {2026},
  doi = {10.1307/mmj/20236356},
  url = {https://doi.org/10.1307/mmj/20236356}
}

@article{Eckl2011,
  author = {Eckl, Thomas},
  title = {{Ciliberto--Miranda} degenerations of {$\mathbb{CP}^2$} blown up in 10 points},
  journal = {Journal of Pure and Applied Algebra},
  volume = {215},
  number = {4},
  pages = {672--696},
  year = {2011},
  doi = {10.1016/j.jpaa.2010.06.016},
  eprint = {0907.4425v1},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://doi.org/10.1016/j.jpaa.2010.06.016}
}

@incollection{CDMR2011,
  author = {Ciliberto, Ciro and Dumitrescu, Olivia and Miranda, Rick and Ro{\'e}, Joaquim},
  title = {Emptiness of homogeneous linear systems with ten general base points},
  booktitle = {Classification of Algebraic Varieties},
  editor = {Faber, Carel and van der Geer, Gerard and Looijenga, Eduard},
  series = {EMS Series of Congress Reports},
  pages = {189--195},
  publisher = {European Mathematical Society},
  address = {Z{\"u}rich},
  year = {2011},
  doi = {10.4171/007-1/8},
  eprint = {0910.1171v1},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://doi.org/10.4171/007-1/8}
}

@article{BM2025,
  author = {Bansal, A. and Majumder, S.},
  title = {Seshadri constants and related conjectures over characteristic zero fields},
  journal = {Bulletin des Sciences Math{\'e}matiques},
  volume = {202},
  pages = {103617},
  year = {2025},
  doi = {10.1016/j.bulsci.2025.103617},
  url = {https://doi.org/10.1016/j.bulsci.2025.103617}
}

@incollection{CHMR2012,
  author = {Ciliberto, Ciro and Harbourne, Brian and Miranda, Rick and Ro{\'e}, Joaquim},
  title = {Variations on {Nagata}'s Conjecture},
  booktitle = {A Celebration of Algebraic Geometry},
  editor = {Hassett, Brendan and McKernan, James and Starr, Jason and Vakil, Ravi},
  series = {Clay Mathematics Proceedings},
  volume = {18},
  pages = {185--203},
  year = {2013},
  publisher = {American Mathematical Society},
  address = {Providence, RI},
  eprint = {1202.0475},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://www.math.colostate.edu/~miranda/preprints/cmip419.pdf}
}

@article{DHKRS2016,
  author = {Dumnicki, Marcin and Harbourne, Brian and K{\"u}ronya, Alex and Ro{\'e}, Joaquim and Szemberg, Tomasz},
  title = {Very general monomial valuations of {$\mathbb{P}^2$} and a {Nagata} type conjecture},
  journal = {Communications in Analysis and Geometry},
  volume = {25},
  number = {1},
  pages = {125--161},
  year = {2017},
  doi = {10.4310/CAG.2017.v25.n1.a4},
  eprint = {1312.5549},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://doi.org/10.4310/CAG.2017.v25.n1.a4}
}

@article{Nivoche2019,
  author = {Nivoche, St{\'e}phanie},
  title = {Transcendental versions in {$\mathbb{C}^n$} of the {Nagata} conjecture},
  journal = {Annales de l'Institut Fourier},
  volume = {71},
  number = {1},
  pages = {27--52},
  year = {2021},
  doi = {10.5802/aif.3402},
  eprint = {1906.08518},
  archivePrefix = {arXiv},
  primaryClass = {math.CV},
  url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3402/}
}

@misc{Stacks,
  author = {{The Stacks Project Authors}},
  title = {The {Stacks} Project},
  year = {2026},
  url = {https://stacks.math.columbia.edu},
  note = {Tags 0B3P (normal bundles), 01XT (cohomology of projective space), and 0C1Z (torsion in the Picard group)},
  urldate = {2026-10-01}
}

@article{Chow1949,
  author = {Chow, W.-L.},
  title = {On compact complex analytic varieties},
  journal = {American Journal of Mathematics},
  volume = {71},
  pages = {893--914},
  year = {1949},
  doi = {10.2307/2372375},
  url = {https://doi.org/10.2307/2372375}
}

@article{CM1998,
  author = {Ciliberto, Ciro and Miranda, Rick},
  title = {Degenerations of planar linear systems},
  journal = {Journal f{\"u}r die reine und angewandte Mathematik},
  volume = {501},
  pages = {191--220},
  year = {1998},
  doi = {10.1515/crll.1998.077},
  eprint = {alg-geom/9702015},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1515/crll.1998.077}
}

@article{Evain2007,
  author = {Evain, Laurent},
  title = {Computing limit linear series with infinitesimal methods},
  journal = {Annales de l'Institut Fourier},
  volume = {57},
  number = {6},
  pages = {1947--1974},
  year = {2007},
  doi = {10.5802/aif.2319},
  eprint = {math/0407143},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2319/}
}

@article{Dumnicki2007,
  author = {Dumnicki, Marcin},
  title = {Cutting diagram method for systems of plane curves with base points},
  journal = {Annales Polonici Mathematici},
  volume = {90},
  number = {2},
  pages = {131--143},
  year = {2007},
  doi = {10.4064/ap90-2-3},
  url = {https://doi.org/10.4064/ap90-2-3}
}

@incollection{Rosengren2020,
  author = {Rosengren, Hjalmar},
  title = {Elliptic hypergeometric functions},
  booktitle = {Lectures on Orthogonal Polynomials and Special Functions},
  editor = {Cohl, Howard S. and Ismail, Mourad E. H.},
  pages = {213--279},
  publisher = {Cambridge University Press},
  year = {2020},
  doi = {10.1017/9781108908993.005},
  eprint = {1608.06161v3},
  archivePrefix = {arXiv},
  primaryClass = {math.CA},
  url = {https://arxiv.org/abs/1608.06161v3},
  note = {Preprint version: arXiv:1608.06161v3}
}