Invaders of the Rokujoma!?

Now that he enters his high school career, Satomi Koutaro begins his life living alone in an apartment that only costs him 5000 yen per month, an extremely cheap deal even for this small apartment. There’s a catch: the apartment is apparently haunted by a cute ghost that has driven its prior occupants away. Next thing he knows, not only is there a ghost trying to drive him out of his new home, but magical girls and other unique female characters turn this small apartment into a battleground of sorts.

Dusk Maiden of Amnesia

60 years ago, a young woman was left to die in the abandoned school building behind the exclusive Seikyou Academy. No one knows why. No one knows how. But the horrifying tale and the legends of the ghostly haunting that followed live on to this day. Perhaps it's not so surprising then, that among Seikyou's many school clubs is one for students interested in "paranormal investigations." What might raise more than a few hairs, however, is that the founder of the club is the ghost herself. Unable to remember how she died and trapped in the grey land between life and death, Yuuko latches onto Teiichi Niiya, a freshman who can inexplicably see her, and together they and the other unsuspecting members of the club begin to unravel the many dark mysteries that surround Seikyou. Will unlocking the secret of Yuuko's gruesome death finally free her? Or will her sudden close association with a mortal have even stranger repercussions on both of their existences? (Source: Sentai Filmworks)

A Certain Magical Index

Set in a city of scientifically advanced superhuman students, but in a world where magic is also real. Touma Kamijou’s right hand, the Imagine Breaker, will negate all magic, psychic, or divine powers, but not his own bad luck. One day he finds a young girl hanging on his balcony railing. She turns out to be a nun from the Church of England, and her mind has been implanted with the Index-Librorum-Prohibitorum - all the magical texts the Church has removed from circulation.

Kubikiri Cycle: The Blue Savant and the Nonsense User

It's the vacation of a lifetime, a trip to a remote island filled with geniuses–and murder. On Wet Crow's Feather Island, a tiny speck in the Sea of Japan, lives Akagami Iria, the exiled daughter of a powerful family. Born into great wealth, she was a princess of the highest pedigree–until she was cut off by the leader of the Akagami Foundation. For the last five years, she's lived on Feather Island with her maids. But she hasn't been alone. She has invited the best minds Japan has to offer to come and stay with her. And so nineteen-year-old college student Ii-chan and his best friend, computer genius Kunagisa Tomo, find themselves as Iria’s guests at her elaborate mansion. Surrounded by fascinating women – a chef, a fortune-teller, a scholar, and an artist, not to mention his own friend Tomo – Ii-chan is feeling a little overmatched intellectually. But the sudden discovery of a grisly murder sends the island into shock. And Ii-chan discovers that he does possess a bit of genius: the ability to discover what is real and what is fake, who is who they claim to be and who is a killer. (Source: Del Rey Manga)