Special Issues

On Nonvanishing for uniruled log canonical pairs

  • Received: 01 November 2020 Revised: 01 April 2021 Published: 26 May 2021
  • Primary: 14E30

  • We prove the Nonvanishing conjecture for uniruled projective log canonical pairs of dimension $ n $, assuming the Nonvanishing conjecture for smooth projective varieties in dimension $ n-1 $. We also show that the existence of good minimal models for non-uniruled projective klt pairs in dimension $ n $ implies the existence of good minimal models for projective log canonical pairs in dimension $ n $.

    Citation: Vladimir Lazić, Fanjun Meng. On Nonvanishing for uniruled log canonical pairs[J]. Electronic Research Archive, 2021, 29(5): 3297-3308. doi: 10.3934/era.2021039

    Related Papers:

  • We prove the Nonvanishing conjecture for uniruled projective log canonical pairs of dimension $ n $, assuming the Nonvanishing conjecture for smooth projective varieties in dimension $ n-1 $. We also show that the existence of good minimal models for non-uniruled projective klt pairs in dimension $ n $ implies the existence of good minimal models for projective log canonical pairs in dimension $ n $.



    加载中


    [1] The moduli $b$-divisor of an lc-trivial fibration. Compos. Math. (2005) 141: 385-403.
    [2] Ascending chain condition for log canonical thresholds and termination of log flips. Duke Math. J. (2007) 136: 173-180.
    [3] On existence of log minimal models II. J. Reine Angew. Math. (2011) 658: 99-113.
    [4] Existence of minimal models for varieties of log general type. J. Amer. Math. Soc. (2010) 23: 405-468.
    [5] The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension. J. Algebraic Geom. (2013) 22: 201-248.
    [6] S. R. Choi, The Geography of Log Models and its Applications, PhD Thesis, Johns Hopkins University, 2008.
    [7] O. Debarre, Higher-Dimensional Algebraic Geometry, Universitext, Springer-Verlag, New York, 2001. doi: 10.1007/978-1-4757-5406-3
    [8] Extension theorems, non-vanishing and the existence of good minimal models. Acta Math. (2013) 210: 203-259.
    [9] A note on the abundance conjecture. Algebraic Geometry (2015) 2: 476-488.
    [10] O. Fujino, Special termination and reduction to pl flips, in Flips for 3-folds and 4-folds (ed. A. Corti), vol. 35 of Oxford Lecture Ser. Math. Appl., Oxford Univ. Press, 2007, 63-75. doi: 10.1093/acprof:oso/9780198570615.003.0004
    [11] O. Fujino, What is log terminal?, in Flips for 3-folds and 4-folds (ed. A. Corti), vol. 35 of Oxford Lecture Ser. Math. Appl., Oxford Univ. Press, 2007, 49-62. doi: 10.1093/acprof:oso/9780198570615.003.0003
    [12] Fundamental theorems for the log minimal model program. Publ. Res. Inst. Math. Sci. (2011) 47: 727-789.
    [13] On canonical bundle formulas and subadjunctions. Michigan Math. J. (2012) 61: 255-264.
    [14] On the minimal model theory for dlt pairs of numerical log Kodaira dimension zero. Math. Res. Lett. (2011) 18: 991-1000.
    [15] Reduction maps and minimal model theory. Compos. Math. (2013) 149: 295-308.
    [16] C. D. Hacon and C. Xu, On finiteness of B-representations and semi-log canonical abundance, in Minimal Models and Extremal Rays (Kyoto, 2011), vol. 70 of Adv. Stud. Pure Math., Math. Soc. Japan, Tokyo, 2016,361–377.
    [17] J. Han and Z. Li, Weak Zariski decompositions and log terminal models for generalized polarized pairs, arXiv: 1806.01234.
    [18] On the non-vanishing conjecture and existence of log minimal models. Publ. Res. Inst. Math. Sci. (2018) 54: 89-104.
    [19] On minimal model theory for log abundant lc pairs. J. Reine Angew. Math. (2020) 767: 109-159.
    [20] Log canonical pairs over varieties with maximal Albanese dimension. Pure Appl. Math. Q. (2016) 12: 543-571.
    [21] Pluricanonical systems on minimal algebraic varieties. Invent. Math. (1985) 79: 567-588.
    [22] Log abundance theorem for threefolds. Duke Math. J. (1994) 75: 99-119.
    [23] Log canonical singularities are Du Bois. J. Amer. Math. Soc. (2010) 23: 791-813.
    [24] (1998) Birational Geometry of Algebraic Varieties, vol. 134 of Cambridge Tracts in Mathematics.Cambridge University Press.
    [25] V. Lazić and Th. Peternell, Abundance for varieties with many differential forms, Épijournal Geom. Algébrique, 2 (2018), Article 1. doi: 10.46298/epiga.2018.volume2.3867
    [26] On Generalised Abundance, II. Peking Math. J. (2020) 3: 1-46.
    [27] V. Lazić and N. Tsakanikas, On the existence of minimal models for log canonical pairs, arXiv: 1905.05576, to appear in Publ. Res. Inst. Math. Sci.
    [28] Y. Miyaoka, The Chern classes and Kodaira dimension of a minimal variety, in Algebraic Geometry, Sendai, 1985, vol. 10 of Adv. Stud. Pure Math., North-Holland, Amsterdam, 1987,449–476. doi: 10.2969/aspm/01010449
    [29] On the Kodaira dimension of minimal threefolds. Math. Ann. (1988) 281: 325-332.
    [30] N. Nakayama, Zariski-Decomposition and Abundance, vol. 14 of MSJ Memoirs, Mathematical Society of Japan, Tokyo, 2004.
    [31] $3$-fold log models. J. Math. Sci. (1996) 81: 2667-2699.
  • Reader Comments
  • © 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(798) PDF downloads(165) Cited by(0)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog