In Japanese folklore and mythology, there are stories of cursed swords, including some katanas. These cursed swords are often depicted as having supernatural powers or being imbued with malevolent spirits. While these tales are rooted in folklore and legends, it's important to note that they are not based on historical facts.

One well-known example is the "Muramasa" sword. Muramasa Sengo was a legendary swordsmith from the 16th century, and his swords are often associated with a curse. According to the legends, Muramasa's swords were said to be exceptionally sharp and deadly but also thirsted for blood and had a malevolent influence on their wielders. It was believed that these swords had a tendency to incite violence and bring misfortune.

Another example is the "Tengu-no-Dachi," a sword associated with the mythical creature known as the Tengu. The Tengu were supernatural beings in Japanese folklore, often depicted as bird-like creatures with magical powers. Legend has it that the Tengu-no-Dachi was a cursed sword that would bring disaster and calamity to its owner.

It's important to remember that these stories of cursed swords are part of folklore and mythology, and their existence in reality is highly doubtful. Curses and supernatural properties attributed to swords are mainly fictional elements created for storytelling and cultural folklore.