  Mechanical deformations, either spontaneously occurring during sample
preparation or purposely induced in their nanoscale manipulation, drastically
affect the electronic and optical properties of transition metal dichalcogenide
monolayers. In this first-principles work based on density-functional theory,
we shed light on the interplay among strain, curvature, and electronic
structure of MoSe$_2$ nanowrinkles. We analyze their structural properties
highlighting the effects of coexisting local domains of tensile and compressive
strain in the same system. By contrasting the band structures of the
nanowrinkles against counterparts obtained for flat monolayers subject to the
same amount of strain, we clarify that the specific features of the former,
such as the moderate variation of the band-gap size and its persisting direct
nature, are ruled by curvature rather than strain. The analysis of the
wave-function distribution indicates strain-dependent localization of the
frontier states in the conduction region while in the valence the sensitivity
to strain is much less pronounced. The discussion about transport properties,
based on the inspection of the effective masses, reveals excellent perspectives
for these systems as active components for (opto)electronic devices.
