Among the myriad of digital signature schemes, Schnorr signatures are a pivotal cryptographic innovation, blending theoretical soundness with practical utility. This article ventures into the intricacies of Schnorr signatures, delineating their genesis, core mechanics, comparative advantages, and real-world applications, particularly in blockchain technology.

The story of Schnorr signatures takes us back to the work of Claus-Peter Schnorr, a cryptographer whose seminal work laid the foundation for this remarkable signature scheme. Conceived long before the advent of contemporary blockchain platforms, the Schnorr Signature Scheme was heralded for its simplicity and efficiency in cryptographic realms.

Schnorr signatures epitomize properties of non-malleability and provable security, grounded in the hardness of the discrete logarithm problem. The algorithm's elegance lies in its capacity to aggregate multiple signatures, making transactions both efficient and secure.

A comparative lens reveals the advantages of Schnorr signatures over other prevalent digital signature schemes, notably the Elliptic Curve Digital Signature Algorithm (ECDSA). Schnorr signatures provide superior scalability, privacy preservation, and robustness against adversarial exploits. The real-world implications of these differential attributes resonate profoundly within the blockchain ecosystem.

The most consequential implementation of Schnorr Signatures today is seen in Bitcoin's Taproot upgrade, which has increased Bitcoin’s transactional privacy and efficiency. Due to the ability to aggregate Schnorr Signatures, Bitcoin block space can be used more efficiently, increasing the scalability of the network.

This can be observed in the facilitation of a more compact representation of multi-signature transactions. In essence, multiple signatures are aggregated into a singular signature, leading to a significant reduction in transaction size and more transactions per block. Moreover, this design increases privacy, as multi-signature transactions become indistinguishable from standard transactions, obfuscating the transactional footprint.

The exploration of Schnorr signatures reveals its crucial role in enhancing the security and efficiency of cryptocurrency transactions. By allowing the aggregation of multiple signatures into a single one, this signature scheme not only saves valuable block space, making transactions faster and more cost-effective but also introduces a layer of privacy that is much needed in the digital transactions realm.

Bitcoin's Taproot upgrade, which introduced Schnorr signatures, is a prime example of how this cryptographic innovation is being harnessed to address real-world challenges blockchain networks face. It showcases a practical step towards better scalability and privacy, which are critical for the mainstream adoption of cryptocurrencies.

Moreover, the benefits of Schnorr signatures are not confined to Bitcoin alone. Other blockchain projects are also looking towards leveraging the advantages of Schnorr signatures, indicating a broader recognition within the cryptocurrency community of the value brought by this signature scheme.

The ease of implementation, coupled with the significant advantages in terms of scalability, privacy, and security, makes Schnorr signatures a promising addition to the toolkit of blockchain developers and a significant advancement in the cryptocurrency ecosystem.