Surfaces of general type with maximal Picard number near the Noether line

2023/06/27 by Nguyen Bin, Bin, Nguyen, Vicente Lorenzo +1
Mathematics · #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2306.15241

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=2χ-6 for every admissible pair (K²,χ) such that χ\not≡ 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=2χ-6+k are constructed for every admissible pair (K²,χ) such that χ≥ 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 they provide infinitely many new examples of algebraic surfaces of general type with maximal Picard number above the Noether line.

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