Geodesic
Geography of Irregular Gorenstein 3–folds
Canadian journal of mathematics, Tome 67 (2015) no. 3, pp. 696-720

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, we study the explicit geography problem of irregular Gorenstein minimal3-folds of general type. We generalize the classical Noether–Castelnuovo type inequalities for irregularsurfaces to irregular 3-folds according to the Albanese dimension.
DOI : 10.4153/CJM-2014-033-0
Mots-clés : 14J30, 3–fold, geography, irregular variety 
Zhang, Tong. Geography of Irregular Gorenstein 3–folds. Canadian journal of mathematics, Tome 67 (2015) no. 3, pp. 696-720. doi: 10.4153/CJM-2014-033-0
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[1] [1] Barja, M. A., Lower bounds of the slope of fibred threefolds. Internat. J. Math. 11(2000), no. 4, 461–491. Google Scholar

[2] [2] Barja, M. A., Generalized Clifford–Severi inequality and the volume of irregular varieties. arxiv:1303.3045v2. Google Scholar

[3] [3] Beauville, A., L'application canonique pour les surfaces de type général. Invent. Math. 55(1979), no. 2, 121–140. http://dx.doi.Org/10.1007/BF01390086 Google Scholar

[4] [4] Birkenhake, C. and Lange, H., Complex abelian varieties. Grundlehren der Mathematischen Wissenschaften, 302, Springer–Verlag, Berlin, 1992. Google Scholar

[5] [5] Bombieri, E., Canonical models of surfaces of general type. Inst. Hautes Études Sci. Publ. Math. 42(1973), 171–219. Google Scholar

[6] [6] Catanese, F., Chen, M., and –Q. Zhang, D., The Noether inequality for smooth minimal 3–folds. Math. Res. Lett. 13(2006), no. 4, 653–666. Google Scholar | DOI

[7] [7] Chen, J. A. and Chen, M., The Noether inequality for Gorenstein minimal 3–folds. arxiv:1310.7709 Google Scholar

[8] [8] Chen, J. A. and Chen, M., Explicit birational geometry of threefolds of general type, I. Ann. Sci. Éc Norm. Super. 43(2010), 365–394. Google Scholar

[9] [9] Chen, J. A., Chen, M., and –Q. Zhang, D., On the 5–canonical system of 3–folds of general type. J Reine Angew. Math. 603(2007), 161–181. Google Scholar

[10] [10] Chen, J. A. and Hacon, C. D., On the geography of threefolds of general type. J. Algebra 321(2009), no. 9, 2500–2507. http://dx.doi.Org/10.1016/j.jalgebra.2009.01.01 2 Google Scholar

[11] [11] Chen, M., Inequalities of Noether type for 3–folds of general type. J. Math. Soc. Japan 56(2004), no. 4, 1131–1155. Google Scholar | DOI

[12] [12] Chen, M., Minimal threefolds of small slope and the Noether inequality for canonically polarized threefolds. Math. Res. Lett. 11(2004), no. 5–6, 833–852. Google Scholar | DOI

[13] [13] Chen, M. and Hacon, C. D., On the geography of Gorenstein minimal 3–folds of general type. Asian J. Math. 10(2006), no. 4, 757–763. Google Scholar | DOI

[14] [14] Debarre, O., Inégalités numériques pour les surfaces de type général. Bull. Soc. Math. France 110(1982), no. 3, 319–346. Google Scholar

[15] [15] di Severi, F., La série canonica e la teoria délie série principali degruppi dipunti sopra una superifcie algebrica. Comment. Math. Helv. 4(1932), no. 1, 268–326. Google Scholar | DOI

[16] [16] Ein, L. and Lazarsfeld, R., Singularities oftheta divisors and the birational geometry of irregular varieties. J. Amer. Math. Soc. 10(1997), no. 1, 243–258. Google Scholar | DOI

[17] [17] Francia, P., On the base points of the bicanonical system. In: Problems in the theory of surfaces and their classification (Cortona, 1988), Sympos. Math., 32, Academic Press, London, 1991, pp. 141–150. Google Scholar

[18] [18] Green, M. and Lazarsfeld, R., Deformation theory, generic vanishing theorems, and some conjectures of Enriques, Catanese and Beauville. Invent. Math. 90(1987), no. 2, 389–407. http://dx.doi.Org/10.1007/BF01388711 Google Scholar

[19] [19] Hacon, C. and Kovâcs, S., Generic vanishing fails for singular varieties and in characteristic p > O. arxiv:1212.5105 +O.+arxiv:1212.5105>Google Scholar

[20] [20] Horikawa, E., Algebraic surfaces of general type with small c2 V. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28(1981), no. 3, 745–755. Google Scholar

[21] [21] Hu, Y., Inequality of Noether type for smooth minimal 3-folds of general type. arxiv:1309.4618 Google Scholar

[22] [22] Hunt, B., Complex manifold geography in dimension 2 and 3. J. Differential Geom. 30(1989), no. 1, 51–153. Google Scholar

[23] [23] Kollâr, J., Higher direct images of dualizing sheaves. I. Ann. of Math. (2) 123(1986), no. 1,11–42. http://dx.doi.Org/10.2307/1971351 Google Scholar

[24] [24] Kollâr, J., Higher direct images of dualizing sheaves. II. Ann. of Math. (2) 124(1986), no. 1, 171–202. http://dx.doi.Org/10.2307/1971390 Google Scholar

[25] [25] Liedtke, C., Algebraic surfaces in positive characteristic. In: Birational geometry, rational curves, and arithmetic. Springer, New York, 2013, pp. 229–292. http://dx.doi.Org/10.1007/978-1-4614-6482-2.11 Google Scholar

[26] [26] Liedtke, C., Algebraic surfaces of general type with small c2 in positive characteristic. Nagoya Math. J. 191(2008), 111–134. Google Scholar

[27] [27] Lu, S. S. Y., On surfaces of general type with maximal Albanese dimension. J. Reine Angew. Math. 641(2010), 163–175. Google Scholar

[28] [28] Lu, S. S. Y., Holomorphic curves on irregular varieties of general type starting from surfaces. In: Affine algebraic geometry, CRM Proc. Lecture Notes, 54, American Mathematical Society, Providence, RI, 2011, pp. 205–220. Google Scholar

[29] [29] Lu, S. S. Y., A uniform bound on the canonical degree of Albanese defective curves on surfaces. Bull. Lond. Math. Soc. 44(2012), no. 6, 1182–1188. http://dx.doi.Org/10.1112/blms/bdsO43 Google Scholar

[30] [30] Miyaoka, Y. The Chern classes and Kodaira dimension of a minimal variety. In: Algebraic Geometry, Sendai, 1985, Adv. Stud. Pure Math., 10, North-Holland, Amsterdam, 1987, pp. 449–476. Google Scholar

[31] [31] Ohno, K., Some inequalities for minimal fibrations of surfaces of general type over curves. J. Math. Soc. Japan 44(1992), no. 4, 643–666. http://dx.doi.Org/10.2969/jmsj704440643 Google Scholar

[32] [32] Pardini, R., The Severi inequality K2 > 4Xfor surfaces of maximal Albanese dimension. Invent. Math. 159(2005), no. 3, 669–672. +4Xfor+surfaces+of+maximal+Albanese+dimension.+Invent.+Math.+159(2005),+no.+3,+669–672.+http://dx.doi.org/10.1007/s00222-004-0399-7>Google Scholar | DOI

[33] [33] Shin, D.-K., Noether inequality for a nef and big divisor on a surface. Commun. Korean Math. Soc. 23(2008), no. 1, 11–18. http://dx.doi.Org/10.4134/CKMS.2008.23.1.011 Google Scholar

[34] [34] Xiao, G., Fibered algebraic surfaces with low slope. Math. Ann. 276(1987), no. 3, 449–466. http://dx.doi.Org/10.1007/BF01450841 Google Scholar

[35] [35] Yuan, X. and Zhang, T., Relative Noether inequality on fibered surfaces. Adv. Math. 259(2014), 89–115. http://dx.doi.Org/10.1016/j.aim.2014.03.018 Google Scholar

[36] [36] Zhang, T., Severi inequality for varieties of maximal Albanese dimension. Math. Ann. 359(2014),no. 3-4, 1097–1114. Google Scholar | DOI

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