{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:47:05Z","timestamp":1740109625969,"version":"3.37.3"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2017,5,11]],"date-time":"2017-05-11T00:00:00Z","timestamp":1494460800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"SNCF","award":["168647"],"award-info":[{"award-number":["168647"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2017,7]]},"DOI":"10.1007\/s00454-017-9894-7","type":"journal-article","created":{"date-parts":[[2017,5,11]],"date-time":"2017-05-11T16:50:55Z","timestamp":1494521455000},"page":"158-179","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Tropical Approach to Nagata\u2019s Conjecture in Positive Characteristic"],"prefix":"10.1007","volume":"58","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1613-5175","authenticated-orcid":false,"given":"Nikita","family":"Kalinin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,5,11]]},"reference":[{"issue":"2","key":"9894_CR1","first-page":"201","volume":"4","author":"J Alexander","year":"1995","unstructured":"Alexander, J., Hirschowitz, A.: Polynomial interpolation in several variables. J. Algebr. Geom. 4(2), 201\u2013222 (1995)","journal-title":"J. Algebr. Geom."},{"issue":"2","key":"9894_CR2","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/s002220000053","volume":"140","author":"J Alexander","year":"2000","unstructured":"Alexander, J., Hirschowitz, A.: An asymptotic vanishing theorem for generic unions of multiple points. Invent. Math. 140(2), 303\u2013325 (2000)","journal-title":"Invent. Math."},{"issue":"3","key":"9894_CR3","first-page":"299","volume":"56","author":"C Bocci","year":"2005","unstructured":"Bocci, C.: Special effect varieties in higher dimension. Collect. Math. 56(3), 299\u2013326 (2005)","journal-title":"Collect. Math."},{"key":"9894_CR4","first-page":"25","volume-title":"Parameter Spaces (Warsaw, 1994). Banach Center Publications","author":"M Brion","year":"1996","unstructured":"Brion, M.: Piecewise polynomial functions, convex polytopes and enumerative geometry. In: Pragacz, P. (ed.) Parameter Spaces (Warsaw, 1994). Banach Center Publications, vol. 36, pp. 25\u201344. Polish Academy of Sciences, Warsaw (1996)"},{"key":"9894_CR5","unstructured":"Brugall\u00e9, E., Itenberg, I., Mikhalkin, G., Shaw, K.: Brief introduction to tropical geometry. In: Akbulut, S. et al. (eds.) Proceedings of the G\u00f6kova Geometry-Topology Conference 2014, pp. 1\u201375. International Press of Boston, Somerville (2015). arXiv:1502.05950"},{"issue":"6","key":"9894_CR6","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1016\/j.crma.2007.07.026","volume":"345","author":"E Brugall\u00e9","year":"2007","unstructured":"Brugall\u00e9, E., Mikhalkin, G.: Enumeration of curves via floor diagrams. C. R. Math. Acad. Sci. Paris 345(6), 329\u2013334 (2007)","journal-title":"C. R. Math. Acad. Sci. Paris"},{"key":"9894_CR7","unstructured":"Brugall\u00e9, E., Mikhalkin, G.: Floor decompositions of tropical curves: the planar case. In: Akbulut, S. et al. (eds.) Proceedings of G\u00f6kova Geometry-Topology Conference 2008, pp. 64\u201390. International Press of Boston, Somerville (2009)"},{"key":"9894_CR8","doi-asserted-by":"crossref","unstructured":"Ciliberto, C.: Geometric aspects of polynomial interpolation in more variables and of Waring\u2019s problem. In: Casacuberta, C. et al. (eds.) European Congress of Mathematics, vol. I (Barcelona, 2000). Progress in Mathematics, vol. 201, pp. 289\u2013316. Birkh\u00e4user, Basel (2001)","DOI":"10.1007\/978-3-0348-8268-2_17"},{"key":"9894_CR9","unstructured":"Ciliberto, C., Harbourne, B., Miranda, R., Ro\u00e9, J.: Variations of Nagata\u2019s conjecture. In: Hassett, B. et al. (eds.) A Celebration of Algebraic Geometry. Clay Mathematics Proceedings, vol. 18, pp. 185\u2013203. American Mathematical Society, Providence (2013)"},{"issue":"4","key":"9894_CR10","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1090\/S1056-3911-2011-00545-6","volume":"20","author":"C Ciliberto","year":"2011","unstructured":"Ciliberto, C., Miranda, R.: Homogeneous interpolation on ten points. J. Algebr. Geom. 20(4), 685\u2013726 (2011)","journal-title":"J. Algebr. Geom."},{"key":"9894_CR11","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1016\/j.aim.2013.10.029","volume":"252","author":"M Dumnicki","year":"2014","unstructured":"Dumnicki, M., Harbourne, B., Szemberg, T., Tutaj-Gasi\u0144ska, H.: Linear subspaces, symbolic powers and Nagata type conjectures. Adv. Math. 252, 471\u2013491 (2014)","journal-title":"Adv. Math."},{"issue":"6","key":"9894_CR12","doi-asserted-by":"crossref","first-page":"1947","DOI":"10.5802\/aif.2319","volume":"57","author":"L Evain","year":"2007","unstructured":"Evain, L.: Computing limit linear series with infinitesimal methods. Ann. Inst. Fourier (Grenoble) 57(6), 1947\u20131974 (2007)","journal-title":"Ann. Inst. Fourier (Grenoble)"},{"issue":"4","key":"9894_CR13","doi-asserted-by":"crossref","first-page":"530","DOI":"10.1006\/ffta.2001.0313","volume":"7","author":"SH Hansen","year":"2001","unstructured":"Hansen, S.H.: Error-correcting codes from higher-dimensional varieties. Finite Fields Appl. 7(4), 530\u2013552 (2001)","journal-title":"Finite Fields Appl."},{"key":"9894_CR14","doi-asserted-by":"crossref","unstructured":"Harbourne, B.: Problems and progress: a survey on fat points in $$\\mathbb{P}^2$$ P 2 . In: Geramita, A.V. (ed.) Zero-Dimensional Schemes and Applications (Naples, 2000). Queen\u2019s Papers in Pure and Applied Mathematics, vol. 123, pp. 85\u2013132. Queen\u2019s University, Kingston (2002)","DOI":"10.4153\/CJM-2000-006-6"},{"key":"9894_CR15","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1016\/j.jcta.2015.09.003","volume":"137","author":"N Kalinin","year":"2016","unstructured":"Kalinin, N.: The Newton polygon of a planar singular curve and its subdivision. J. Comb. Theory Ser. A 137, 226\u2013256 (2016)","journal-title":"J. Comb. Theory Ser. A"},{"issue":"16","key":"9894_CR16","doi-asserted-by":"crossref","first-page":"3189","DOI":"10.1215\/00127094-3673558","volume":"165","author":"E Katz","year":"2016","unstructured":"Katz, E., Rabinoff, J., Zureick-Brown, D.: Uniform bounds for the number of rational points on curves of small Mordell\u2013Weil rank. Duke Math. J. 165(16), 3189\u20133240 (2016)","journal-title":"Duke Math. J."},{"key":"9894_CR17","doi-asserted-by":"crossref","unstructured":"Maclagan, D., Sturmfels, B.: Introduction to Tropical Geometry. Graduate Studies in Mathematics, vol. 161. American Mathematical Society, Providence (2015)","DOI":"10.1090\/gsm\/161"},{"issue":"1","key":"9894_CR18","first-page":"79","volume":"68","author":"T Markwig","year":"2010","unstructured":"Markwig, T.: A field of generalised Puiseux series for tropical geometry. Rend. Semin. Mat. Univ. Politec. Torino 68(1), 79\u201392 (2010)","journal-title":"Rend. Semin. Mat. Univ. Politec. Torino"},{"issue":"4","key":"9894_CR19","first-page":"879","volume":"48","author":"H Markwig","year":"2012","unstructured":"Markwig, H., Markwig, T., Shustin, E.: Tropical surface singularities. Discrete Comput. Geom. 48(4), 879\u2013914 (2012)","journal-title":"Discrete Comput. Geom."},{"issue":"2","key":"9894_CR20","first-page":"192","volume":"46","author":"R Miranda","year":"1999","unstructured":"Miranda, R.: Linear systems of plane curves. Notices Am. Math. Soc. 46(2), 192\u2013201 (1999)","journal-title":"Notices Am. Math. Soc."},{"issue":"3","key":"9894_CR21","doi-asserted-by":"crossref","first-page":"766","DOI":"10.2307\/2372927","volume":"81","author":"M Nagata","year":"1959","unstructured":"Nagata, M.: On the $$14$$ 14 -th problem of Hilbert. Am. J. Math. 81(3), 766\u2013772 (1959)","journal-title":"Am. J. Math."},{"issue":"5","key":"9894_CR22","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1016\/j.jpaa.2012.09.019","volume":"217","author":"S Paul","year":"2013","unstructured":"Paul, S.: New methods for determining speciality of linear systems based at fat points in $${\\mathbb{P}}^n$$ P n . J. Pure Appl. Algebra 217(5), 927\u2013945 (2013)","journal-title":"J. Pure Appl. Algebra"},{"key":"9894_CR23","doi-asserted-by":"crossref","unstructured":"Ruiz, J.M.: The Basic Theory of Power Series. Advanced Lectures in Mathematics. Friedr. Vieweg & Sohn, Braunschweig (1993)","DOI":"10.1007\/978-3-322-84994-6"},{"issue":"1","key":"9894_CR24","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1137\/09075024X","volume":"24","author":"R Steffens","year":"2010","unstructured":"Steffens, R., Theobald, T.: Combinatorics and genus of tropical intersections and Ehrhart theory. SIAM J. Discrete Math. 24(1), 17\u201332 (2010)","journal-title":"SIAM J. Discrete Math."},{"issue":"2\u20133","key":"9894_CR25","first-page":"405","volume":"30","author":"B Strycharz-Szemberg","year":"2004","unstructured":"Strycharz-Szemberg, B., Szemberg, T.: Remarks on the Nagata conjecture. Serdica Math. J. 30(2\u20133), 405\u2013430 (2004)","journal-title":"Serdica Math. J."},{"key":"9894_CR26","doi-asserted-by":"crossref","unstructured":"Tsfasman, M., Vl\u0103du\u0163, S., Nogin, D.: Algebraic Geometric Codes: Basic Notions. Mathematical Surveys and Monographs, vol. 139. American Mathematical Society, Providence (2007)","DOI":"10.1090\/surv\/139"},{"issue":"5","key":"9894_CR27","doi-asserted-by":"crossref","first-page":"1783","DOI":"10.4171\/JEMS\/403","volume":"15","author":"I Tyomkin","year":"2013","unstructured":"Tyomkin, I.: On Zariski\u2019s theorem in positive characteristic. J. Eur. Math. Soc. (JEMS) 15(5), 1783\u20131803 (2013)","journal-title":"J. Eur. Math. Soc. (JEMS)"},{"issue":"3","key":"9894_CR28","doi-asserted-by":"crossref","first-page":"439","DOI":"10.4310\/jdg\/1214460859","volume":"48","author":"J Wahl","year":"1998","unstructured":"Wahl, J.: Nodes on sextic hypersurfaces in $$\\mathbf{P}^3$$ P 3 . J. Differ. Geom. 48(3), 439\u2013444 (1998)","journal-title":"J. Differ. Geom."},{"issue":"4","key":"9894_CR29","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1007\/BF01459801","volume":"299","author":"G Xu","year":"1994","unstructured":"Xu, G.: Curves in $$\\mathbf{P}^2$$ P 2 and symplectic packings. Math. Ann. 299(4), 609\u2013613 (1994)","journal-title":"Math. Ann."}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-017-9894-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-017-9894-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-017-9894-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,24]],"date-time":"2019-09-24T10:02:53Z","timestamp":1569319373000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-017-9894-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,5,11]]},"references-count":29,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,7]]}},"alternative-id":["9894"],"URL":"https:\/\/doi.org\/10.1007\/s00454-017-9894-7","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"type":"print","value":"0179-5376"},{"type":"electronic","value":"1432-0444"}],"subject":[],"published":{"date-parts":[[2017,5,11]]}}}