Abstract
We give an estimation for the arithmetic genus of an integral space curve which is not contained in a surface of degree k−1. Our main technique is the Bogomolov-Gieseker type inequality for ℙ3 proved by Macrì.
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References
A. Bayer, A. Bertram, E. Macrì, Y. Toda: Bridgeland stability conditions of threefolds II: An application to Fujita’s conjecture. J. Algebr. Geom. 23 (2014), 693–710.
A. Bayer, E. Macrì, P. Stellari: The space of stability conditions on abelian threefolds, and on some Calabi-Yau threefolds. Invent. Math. 206 (2016), 869–933.
A. Bayer, E. Macrì, Y. Toda: Bridgeland stability conditions on threefolds I: Bogomolov-Gieseker type inequalities. J. Algebr. Geom. 23 (2014), 117–163.
T. Bridgeland: Stability conditions on triangulated categories. Ann. of Math. (2) 166 (2007), 317–345.
G. Castelnuovo: Sui multipli di una serie lineare di gruppi di punti appartenente ad una curva algebrica. Palermo Rend. 7 (1893), 89–110. (In Italian.)
L. Gruson, C. Peskine: Genre des courbes de l’espace projectif. Algebraic Geometry. Proc., Tromsø Symp. 1977, Lect. Notes Math. 687, (1978), pp. 31–59. (In French.)
G. Halphen: Mèmoire sur la classification des courbes gauches algèbriques. J. Ec. Polyt. 52 (1882), 1–200. (In French.)
D. Happel, I. Reiten, S. O. Smalø: Tilting in abelian categories and quasitilted algebras. Mem. Am. Math. Soc. 575 120 (1996), 88 pages.
J. Harris: The genus of space curves. Math. Ann. 249 (1980), 191–204.
R. Hartshorne: On the classification of algebraic space curves II. Algebraic Geometry. Proc. Summer Res. Inst., Brunswick/Maine 1985, part 1, Proc. Symp. Pure Math. 46, 1987, pp. 145–164.
R. Hartshorne, A. Hirschowitz: Nouvelles courbes de bon genre dans l’espace projectif. Math. Ann. 280 (1988), 353–367. (In French.)
A. Maciocia: Computing the walls associated to Bridgeland stability conditions on projective surfaces. Asian J. Math. 18 (2014), 263–280.
E. Macrì: A generalized Bogomolov-Gieseker inequality for the three-dimensional projective space. Algebra Number Theory 8 (2014), 173–190.
Y. Toda: Bogomolov-Gieseker-type inequality and counting invariants. J. Topol. 6 (2013), 217–250.
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The research has been supported by National Natural Science Foundation of China (No. 11301201).
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Sun, H. Arithmetic genus of integral space curves. Czech Math J 68, 1079–1089 (2018). https://doi.org/10.21136/CMJ.2017.0093-17
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DOI: https://doi.org/10.21136/CMJ.2017.0093-17