Surfaces of General Type with Maximal Picard Number Near the Noether Line Articles uri icon

authors

  • BIN, NGUYEN
  • LORENZO GARCIA, VICENTE

publication date

  • June 2024

start page

  • 9792

end page

  • 9807

issue

  • 12

volume

  • 2024

International Standard Serial Number (ISSN)

  • 1073-7928

Electronic International Standard Serial Number (EISSN)

  • 1687-0247

abstract

  • The first published non-trivial examples of algebraic surfaces of general type with maximal Picard number are due to Persson, who constructed surfaces with maximal Picard number on the Noether line K2=2X-6 for every admissible pair (K2,X) such that X=/0 mod 6⁠. In this note, given a non-negative integer k⁠, algebraic surfaces of general type with maximal Picard number lying on the line k2=2x-6+k are constructed for every admissible pair (k2,x) such that x >=2k+10⁠. These constructions, obtained as bidouble covers of rational surfaces, not only allow to fill in Persson"s gap on the Noether line, but also provide infinitely many new examples of algebraic surfaces of general type with maximal Picard number above the Noether line.

subjects

  • Computer Science