Convex Fujita numbers: projective bundles

• Chen, Jiaming ^[1] ; Küronya, Alex ^[1] ; Stix, Jakob ^[1] ; Mustopa, Yusuf ^[2]
  1. [1] Goethe University Frankfurt

     Goethe University Frankfurt

     Frankfurt, Alemania

     
  2. [2] University of Massachusetts Boston

     University of Massachusetts Boston

     City of Boston, Estados Unidos

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 77, Fasc. 2, 2026, págs. 337-354
• Idioma: inglés
• DOI: 10.1007/s13348-025-00471-1
• Texto completo no disponible (Saber más ...)
• Resumen

  • We study effective global generation properties of projectivizations of curve semistable vector bundles over curves and abelian varieties.

• Referencias bibliográficas
  • Angehrn, U., Siu, Y.T.: Effective freeness and point separation for adjoint bundles. Invent. Math. 122(2), 291–308 (1995)
  • Biswas, Indranil, Bruzzo, U.: On semistable principal bundles over a complex projective manifold. Int. Math. Res. Not. 2008, rnn035 (2008)
  • Bruzzo, U., Ruipérez, D.H.: Semistability. Differ. Geom. Appl. 24(4), 403–416 (2006)
  • Balaji, V., Kollár, J.: Holonomy groups of stable vector bundles. Publ. Res. Inst. Math. Sci. 44(2), 183–211 (2008)
  • Bauer, T., Szemberg, T.: On tensor products of ample line bundles on abelian varieties. Math. Z. 223(1), 79–85 (1996)
  • Butler, D.C.: Normal generation of vector bundles over a curve. J. Differ. Geom. 39(1), 1–34 (1994)
  • Chen, J., Küronya, A., Mustopa, Y., Stix, J.: Convex Fujita numbers and the fundamental group. Adv. Geom. 24(4), 577–590 (2024). https://doi-org.sire.ub.edu/10.1515/advgeom-2024-0029
  • Chen, J., Küronya, A., Mustopa, Y., Stix, J.: Convex Fujita numbers and the Kodaira–Enriques classification of surfaces (2023)
  • Ein, L., Lazarsfeld, R.: Global generation of pluricanonical and adjoint linear series on smooth projective threefolds. J. Am. Math. Soc....
  • Fujita, T.: On polarized manifolds whose adjoint bundles are not semipositive. Algebr. Geom. 1985(10), 167–179 (1987)
  • Ghidelli, L., Lacini, J.: Logarithmic bounds on Fujita’s conjecture (2021)
  • Grothendieck, A. (ed.): Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux. Fasc. I: Exposés 1–8; Fasc....
  • Hartshorne, R.: Ample Subvarieties of Algebraic Varieties. Lecture Notes in Mathematics, vol. 156. Springer, Berlin (1970)
  • Heier, G.: Effective freeness of adjoint line bundles. Doc. Math. 7, 31–42 (2002)
  • Huybrechts, D., Lehn, M.: The Geometry of Moduli Spaces of Sheaves, 2nd edn. Cambridge University Press, Cambridge (2010)
  • Jahnke, P., Radloff, I.: Semistability of restricted tangent bundles and a question of I. Biswas. Int. J. Math. 24(1), 1250122 (2013)
  • Kawamata, Y.: On Fujita’s freeness conjecture for 3-folds and 4-folds. Math. Ann. 308(3), 491–505 (1997)
  • Küronya, A., Mustopa, Y.: Continuous CM-regularity of semihomogeneous vector bundles. Adv. Geom. 20(3), 401–412 (2020)
  • Küronya, A., Mustopa, Y.: Effective global generation on varieties with numerically trivial canonical class (2021). arXiv:1810.07079 [math]
  • Kobayashi, S.: Curvature and stability of vector bundles. Proc. Jpn. Acad. Ser. A, Math. Sci. 58(4), 158–162 (1982)
  • Kobayashi, S.: Differential Geometry of Complex Vector Bundles, Publications of the Mathematical Society of Japan, vol. 15, Princeton University...
  • Lazarsfeld, R.: Positivity in Algebraic Geometry. I, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys...
  • Miyaoka, Y.: The Chern classes and Kodaira Dimension of a minimal variety. Algebr. Geom. 1985(10), 449–477 (1987)
  • Misra, Snehajit, Ray, N.: Nef cones of projective bundles over surfaces and Seshadri constants. Osaka J. Math. 59(3), 639–651 (2022)
  • Mukai, S.: Semi-homogeneous vector bundles on an Abelian variety. J. Math. Kyoto Univ. 18(2), 239–272 (1978)
  • Nakayama, N.: Normalized tautological divisors of semi-stable vector bundles, Sūrikaisekikenkyūsho Kokyūroku, pp. 167–173 (1999)
  • Narasimhan, M.S., Ramanan, S.: Moduli of vector bundles on a compact Riemann surface. Ann. Math. Second Ser. 89, 14–51 (1969)
  • Pareschi, G., Popa, M.: Regularity on abelian varieties. I. J. Am. Math. Soc. 16, 285–302 (2003)
  • Reider, I.: Vector bundles of rank 2 and linear systems on algebraic surfaces. Ann. Math. Second Ser. 127(2007055), 309–316 (1988)
  • Ramanan, S., Ramanathan, A.: Some remarks on the instability flag. Tohoku Math. J. 36(2), 269–291 (1984)
  • Umemura, Hiroshi: Some results in the theory of vector bundles. Nagoya Math. J. 52(none), 97–128 (1973)
  • Ye, F., Zhu, Z.: On Fujita’s freeness conjecture in dimension 5. Adv. Math. 371(107210), 56 (2020)