Xiao, Gang Fibered algebraic surfaces with low slope. (English) Zbl 0596.14028 Math. Ann. 276, 449-466 (1987). One studies the properties of a complex surface of general type with a fibration \(f:\quad S\to C\) such that \(\omega^ 2_{S/C}<4\cdot \deg (f_*\omega_{S/C})\). For such a surface the image of the \(\pi_ 1\) of a fibre of f in \(\pi_ 1(S)\) is trivial, unless the fibres of f are hyperelliptic, and this image is \({\mathbb{Z}}_ 2\). One also shows a lower bound for \(\omega^ 2_{S/C}\), studies the stability of \(f_*\omega_{S/C}\), and gives several examples. Cited in 19 ReviewsCited in 96 Documents MSC: 14J25 Special surfaces 14E20 Coverings in algebraic geometry Keywords:fibered algebraic surfaces with low slope; image of fundamental groups PDFBibTeX XMLCite \textit{G. Xiao}, Math. Ann. 276, 449--466 (1987; Zbl 0596.14028) Full Text: DOI EuDML References: [1] Barth, W.-Peters, C.-Van de Ven, A.: Compact complex surfaces. Berlin, Heidelberg, New York: Springer 1984 · Zbl 0718.14023 [2] Beauville, A.: Sur le nombre de points doubles d’une surface dansP 3(?(5)=31). In: Algebraic geometry, Anger 1979. Alphen an de Rijn: Sijthoff and Noordhoff 1980 · Zbl 0445.14016 [3] Beauville, A.: L’inégalitép g ?2q?4 pour les surfaces de type général, Appendix to Debarre, O.: Inégalités numériques pour les surfaces de type général. Bull. Soc. Math. Fr.110, 319-346 (1982) [4] Catanese, F.: Moduli of surfaces of general type. In: Algebraic geometry ? open problems. Lect. Notes Math. 997. Berlin, Heidelberg, New York: 1983 · Zbl 0517.14011 [5] Fujita, T.: On Kähler fiber spaces over surves, J. Math. Soc. Japan30, 779-794 (1978) · Zbl 0393.14006 · doi:10.2969/jmsj/03040779 [6] Harder, G.-Narasimhan, M.S.: On the cohomology groups of moduli spaces of vector bundles on curves. Math. Ann,212,215 (1974) · Zbl 0324.14006 [7] Hartshone, R.: Curves with high self-intersection on algebraic surfaces. Publ. Math. IHES36, 111-125 (1969) · Zbl 0197.17505 [8] Hartshorne, R.: Ample vector bundles on curves. Nagoya Math. J.43, 73-89 (1971) · Zbl 0218.14018 [9] Horikawa, E.: Algebraic surfaces of general type with smallc 1 2 ,V. J. Fac. Sci. Univ. Tokyo Sect. A28, 745-755 (1981) · Zbl 0505.14028 [10] Persson, U.: Double coverings and surfaces of general type. In: Algebraic geometry. Lect. Notes Math.687, Berlin, Heidelberg, New York: Springer 1978 · Zbl 0396.14003 [11] Persson, U.: Chern invariants of surfaces of general type. Compo. Math.43, 3-58 (1981) · Zbl 0479.14018 [12] Reid, M.: 466-2 for surfaces with smallc 1 2 . In: Algebraic geometry, pp. 534-544. Lect. Notes Math.732, Berlin, Heidelberg, New York: Springer 1978 [13] Severi, F.: La serie canonica e la teoria delle serie principali dei gruppi di punti sopra una superficie algebrica. Comment. Math. Helv.4, 268-326 (1932) · Zbl 0005.17602 · doi:10.1007/BF01202721 [14] Xiao, G.: Surfaces fibrées en courbes de genre deux. Lect. Notes Math. 1137. Springer 1985 · Zbl 0579.14028 [15] Xiao, G.: Hyperelliptic surfaces of general type withK 2<4?. Preprint [16] Xiao, G.: Algebraic surfaces with high canonical degree. Math. Ann.274, 473-483 (1986) · Zbl 0571.14019 · doi:10.1007/BF01457229 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.