Sheaf of modulesIn mathematics, a sheaf of O-modules or simply an O-module over a ringed space (X, O) is a sheaf F such that, for any open subset U of X, F(U) is an O(U)-module and the restriction maps F(U) → F(V) are compatible with the restriction maps O(U) → O(V): the restriction of fs is the restriction of f times that of s for any f in O(U) and s in F(U). The standard case is when X is a scheme and O its structure sheaf. If O is the constant sheaf , then a sheaf of O-modules is the same as a sheaf of abelian groups (i.
Spirit (rover)Spirit, also known as MER-A (Mars Exploration Rover – A) or MER-2, is a Mars robotic rover, active from 2004 to 2010. Spirit was operational on Mars for sols or 3.3 Martian years ( days; ). It was one of two rovers of NASA's Mars Exploration Rover Mission managed by the Jet Propulsion Laboratory (JPL). Spirit landed successfully within the impact crater Gusev on Mars at 04:35 Ground UTC on January 4, 2004, three weeks before its twin, Opportunity (MER-B), which landed on the other side of the planet.
Opportunity (rover)Opportunity, also known as MER-B (Mars Exploration Rover – B) or MER-1, is a robotic rover that was active on Mars from 2004 until 2018. Opportunity was operational on Mars for sols ( on Earth). Launched on July 7, 2003, as part of NASA's Mars Exploration Rover program, it landed in Meridiani Planum on January 25, 2004, three weeks after its twin, Spirit (MER-A), touched down on the other side of the planet. With a planned 90-sol duration of activity (slightly less than 92.
Nef line bundleIn algebraic geometry, a line bundle on a projective variety is nef if it has nonnegative degree on every curve in the variety. The classes of nef line bundles are described by a convex cone, and the possible contractions of the variety correspond to certain faces of the nef cone. In view of the correspondence between line bundles and divisors (built from codimension-1 subvarieties), there is an equivalent notion of a nef divisor. More generally, a line bundle L on a proper scheme X over a field k is said to be nef if it has nonnegative degree on every (closed irreducible) curve in X.
Mars Exploration RoverNASA's Mars Exploration Rover (MER) mission was a robotic space mission involving two Mars rovers, Spirit and Opportunity, exploring the planet Mars. It began in 2003 with the launch of the two rovers to explore the Martian surface and geology; both landed on Mars at separate locations in January 2004. Both rovers far outlived their planned missions of 90 Martian solar days: MER-A Spirit was active until March 22, 2010, while MER-B Opportunity was active until June 10, 2018.
