Holomorphic curves whose domains are Riemann surfaces

TL;DR

This paper proves a defect relation for holomorphic curves from open Riemann surfaces into complex projective varieties, focusing on those with Zariski-dense images intersecting divisors.

Contribution

It extends defect relations to holomorphic curves from general open Riemann surfaces into projective varieties, broadening previous results.

Findings

Established a defect relation for holomorphic curves from Riemann surfaces

Applied the relation to curves with Zariski-dense images intersecting divisors

Extended classical results to more general domain surfaces

Abstract

We establish a defect relation of holomorphic curves from a general open Riemann surface into a normal complex projective variety, with Zariski-dense image intersecting effective Cartier divisors.