The Gross-Zagier formula on singular moduli for Shimura curves

Key Points

• This generalization provides a calculation of intersection multiplicity to higher-dimensional spaces.
• The study shows a connection between CM divisors and the geometry of shimura curves through singular moduli.
• The findings reveal deeper relationships between number theory and algebraic geometry related to modular curves.
• This work paves the way for future explorations in the properties of shimura curves and their divisors.