On quasi-polarized manifolds whose sectional genus is equal to the irregularity

 Access to full text

1. [1] A. Beauville, L’inegalite $p_g\ge 2q-4$ pour les surfaces de type général, Bull. Soc. Math. France, 110 (1982), pp. 343–346. Zbl0543.14026MR688038
2. [2] M. C. Beltrametti - A. J. Sommese, The adjunction theory of complex projective varieties, de Gruyter Expositions in Math. 16, Walter de Gruyter, Berlin, NewYork (1995). Zbl0845.14003MR1318687
3. [3] J. P. Demaily, Effective bounds for very ample line bundles, Invent. Math., 124 (1996), pp. 243–261. Zbl0862.14004MR1369417
4. [4] H. Esnault - E. Viehweg, Effective bounds for semipositive sheaves and for the height of points on curves over complex function fields, Composit. Math., 76 (1990), pp. 69–85. Zbl0742.14020MR1078858
5. [5] T. Fujita, On the structure of polarized varieties with $\Delta$ -genera zero, J. Fac. Sci. Univ. of Tokyo, 22 (1975), pp. 103–115. Zbl0333.14004MR369363
6. [6] T. Fujita, Remarks on quasi-polarized varieties, Nagoya Math. J., 115 (1989), pp. 105–123. Zbl0699.14002MR1018086
7. [7] T. Fujita, Classification Theories of Polarized Varieties, London Math. Soc. Lecture Note Ser., 155, Cambridge University Press (1990). Zbl0743.14004MR1162108
8. [8] Y. Fukuma, On polarized surfaces $(X,L)$ with $h^0\left(L\right)gt;0$ , $\kappa \left(X\right)=2$ , and $g\left(L\right)=q\left(X\right),$ Trans. Amer. Math. Soc., 348 (1996), pp. 4185–4197. Zbl0878.14005MR1370640
9. [9] Y. Fukuma, A lower bound for the sectional genus of quasi-polarized surfaces, Geom. Dedicata, 64 (1997), pp. 229–251. Zbl0897.14008MR1436766
10. [10] Y. Fukuma, A lower bound for sectional genus of quasi-polarized manifolds, J. Math. Soc. Japan, 49 (1997), pp. 339–362. Zbl0899.14003MR1601389
11. [11] Y. Fukuma, On the nonemptiness of the linear system of polarized manifolds, Canad. Math. Bull., 41 (1998), pp. 267–278. Zbl0955.14040MR1637645
12. [12] Y. Fukuma, On sectional genus of quasi-polarized $3$ -folds, Trans. Amer. Math. Soc., 351 (1999), pp. 363–377. Zbl0905.14003MR1487615
13. [13] Y. Fukuma, On the sectional geometric genus of quasi-polarized varieties, II, Manuscripta Math., 113 (2004), pp. 211–237. Zbl1080.14013MR2128547
14. [14] Y. Fukuma, A lower bound for sectional genus of quasi-polarized manifolds, II, preprint, http://www.math.kochi-u.ac.jp/fukuma/preprint.html Zbl0899.14003MR1601389
15. [15] A. Höring, On a conjecture of Beltrametti and Sommese, arXiv:0912.1295, to appear in J. Algebraic Geom. Zbl1253.14007
16. [16] A. Höring, The sectional genus of quasi-polarised varieties, Arch. Math., 95 (2010), pp. 125–133. Zbl1198.14008MR2674248
17. [17] A. J. Sommese, On the adjunction theoretic structure of projective varieties, Complex analysis and algebraic geometry (Göttingen, 1985), pp. 175–213, Lecture Notes in Math., 1194 (Springer, Berlin, 1986). Zbl0601.14029MR855885