Infinitely many new sequences of surfaces of general type with maximal Picard number converging to the Severi line

TL;DR

This paper constructs infinitely many new sequences of algebraic surfaces of general type with maximal Picard number, whose invariants approach the Severi line, expanding known examples beyond previous limited cases.

Contribution

It introduces novel sequences of surfaces with maximal Picard number converging to the Severi line, filling gaps in the existing literature.

Findings

Constructed infinitely many new sequences of surfaces.

Invariants of these surfaces converge to the Severi line.

Surfaces have maximal Picard number.

Abstract

Examples of algebraic surfaces of general type with maximal Picard number are not abundant in the literature. Moreover, most known examples either possess low invariants, lie near the Noether line $K^2=2\chi-6$ or are somewhat scattered. A notable exception is Persson's sequence of double covers of the projective plane with maximal Picard number, whose invariants converge to the Severi line $K^2=4\chi$. This note is devoted to the construction of infinitely many new sequences of surfaces of general type with maximal Picard number whose invariants converge to the Severi line.