Cutting insert, cutting tool, and method for manufacturing machined product

A cutting insert comprising:

• an upper surface;
• a lower surface located on an opposite side of the upper surface;
• a lateral surface located between the upper surface and the lower surface;
• and
• a cutting edge located at an intersection of the upper surface and the lateral surface, wherein
• in a case that a virtual axis that passes through a center of the upper surface and a center of the lower surface is set as an insert central axis, and a virtual flat surface that is located between the upper surface and the lower surface and orthogonal to the insert central axis is set as a reference plane,
• the upper surface comprises
• an outer edge comprising a corner portion having a protrusively curved shape and a side portion having a linear shape and extending from the corner portion,
• a land surface located along the outer edge, and
• a main rake surface located along the land surface and having a linear shape, in a first cross section orthogonal to the outer edge, that is closer to the reference plane as farther away from the land surface,
• the land surface comprises
• a first land surface located along the corner portion, and
• a second land surface located along the side portion,
• the first land surface comprises a first linear portion having a linear shape in a second cross section orthogonal to the corner portion, and
• the second land surface has a protrusively curved shape as a whole in a third cross section orthogonal to the side portion.