References
Angehrn, U., Siu, Y.-T.: Effective freeness and point separation for adjoint bundles. Invent. Math. 122, 291–308 (1995)
Benveniste, X.: Sur les applications pluricanoniques des variétés de type très général en dimension 3. Am. J. Math.108, 433–449 (1986)
Bombieri, E.: Canonical models of surfaces of general type. Publ. Math. Inst. Hautes Étud. Sci. 42, 171–219 (1973)
Demailly, J.-P.: A numerical criterion for very ample line bundles. J. Differ. Geom. 37, 323–374 (1993)
Demailly, J.-P., Ein, L., Lazarsfeld, R.: A subadditivity property of multiplier ideals. Mich. Math. J. 48, 137–156 (2000)
Ein, L., Küchle, O., Lazarsfeld, R.: Local positivity of ample line bundles. J. Differ. Geom. 42, 193–219 (1995)
Fujino, O., Mori, S.: A canonical bundle formula. J. Differ. Geom. 56, 167–188 (2000)
Fujita, T.: Approximating Zariski decomposition of big line bundles. Kodai Math. J. 17, 1–3 (1994)
Hanamura, M.: Pluricanonical maps of minimal 3-folds. Proc. Japan Acad., Ser. A, Math. Sci. 61, 116–118 (1985)
Hacon, C., McKernan, J.: Boundedness of pluricanonical maps of varieties of general type. arXiv:math.AG/0504327
Kawamata, Y.: On Fujita’s freeness conjecture for 3-folds and 4-folds. Math. Ann. 308, 491–505 (1997)
Kawamata, Y.: Subadjunction of log canonical divisors II. Am. J. Math. 120, 893–899 (1998)
Kawamata, Y.: Deformations of canonical singularities. J. Am. Math. Soc. 12, 85–92 (1999)
Kawamata, Y., Matsuda K., Matsuki K.: Introduction to the minimal model problem. Algebraic Geometry (Sendai, 1985), Advanced Studies in Pure Math., vol. 10, pp. 283–360. North-Holland 1987
Kodaira, K.: Pluricanonical systems on algebraic surfaces of general type. J. Math. Soc. Japan 30, 170–192 (1968)
Kollár, J.: Effective base point freeness. Math. Ann. 296, 595–605 (1993)
Kollár, J.: Rational curves on algebraic varieties. Ergebnisse der Math. und ihrer Grenzgebiete (3), vol. 32. Berlin: Springer 1996
Kollár, J.: Singularities of pairs. Algebraic Geometry (Santa Cruz, 1995). Proc. Symp. Pure Math., vol. 62, part 1, pp. 221–287. American Mathematical Society 1997
Lazarsfeld, R.: Positivity in algebraic geometry I, II. Ergebnisse der Math. und ihrer Grenzgebiete (3), vol. 48–49. Berlin: Springer 2004
Matsuki, K: On pluricanonical maps for 3-folds of general type. J. Math. Soc. Japan 38, 339–359 (1986)
Nakayama, N.: Zariski-decomposition and abundance. MSJ Memoirs, vol. 14. Mathematical Society Japan 2004
Raynaud, M.: Flat modules in algebraic geometry. Compos. Math. 24, 11–31 (1972)
Reider, I: Vector bundles of rank 2 and linear systems on algebraic surfaces. Ann. Math. 127, 309–316 (1988)
Siu, Y.-T.: Invariance of plurigenera. Invent. Math. 134, 661–673 (1998)
Siu, Y.-T.: Extension of twisted pluricanonical sections with plurisubharmonic weight and invariance of semi-positively twisted plurigenera for manifolds not necessarily of general type. Complex Geometry (Göttingen, 2000), pp. 223–277, ed. by I. Bauer. Berlin: Springer 2002
Tsuji, H.: Pluricanonical systems of projective varieties of general type, v1–v10 (1999–2004) arXiv:math.AG/9909021
Tsuji, H.: Subadjunction theorem for pluricanonical divisors, v1–v2 (2001–2002) arXiv:math.AG/0111311
Tsuji, H.: Pluricanonical systems of projective varieties of general type I. The former half of [T99 ], (2004). A private communication on April 20, 2005
Tsuji, H.: Pluricanonical systems of projective varieties of general type II. A transcription of the latter half of [T99 ], v1–v5 (2004–2005) arXiv:math.CV/0409318
Viehweg, E.: Weak positivity and the additivity of the Kodaira dimension for certain fibre spaces, Advanced Studies in Pure Math., vol. 1, pp. 329–353. North-Holland 1983
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Takayama, S. Pluricanonical systems on algebraic varieties of general type. Invent. math. 165, 551–587 (2006). https://doi.org/10.1007/s00222-006-0503-2
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DOI: https://doi.org/10.1007/s00222-006-0503-2