Couple of points:
1) Gravity is now largely believed, (according to Einstein) to be a "psuedo-force" Not a real force like the push of a rocket engine. It is the result of the geometry of the underlying dimensional manifold.
If a piece of paper is curved, then a line drawn on it will also curve, unless you leave the manifold (paper) altogether.
2) For planets and stars, the mass of the object alters the curvature of the manifold, the space AND time of the underlying space. This curvature is actually quite slight. For the earth, it works out to something like curving a straight line into a loop about a light year in diameter. The mathematics used to describe the curvature of the space-time manifold references it to a flat one.
3) Our experiences give us objects like spheres, which are two dimensional surfaces (or manifold) embedded in a 3 dimensional manifold. But what we can measure, with present technologies and information, is the "intrinsic curvature" of the manifold. This intrinsic curvature tells us NOTHING about the existence or dimensionality, or even the shape, of any higher dimensional manifolds that may or may not exist. They are unnecessary, (unless you want to make use of alledged shortcuts through higher dimensional space)
4) Instead of an umbrella, what you are looking for is a "lens". Something that will curve the manifold differently than what it is. To go up, instead of curving space-time one way, curve it the other, or flatten that curvature out.
5) Because of space-time's rather unique properties, it is not a "thing" like planets and stars. One has no reference point to base a measurement system on, if you refer to the space itself. You can't see it, or touch it, or differentiate one piece of space time from any other, without objects being embedded in that manifold, like rocks, planets, or stars.
6) Anti-gravity mines, or gravity nullification mines: As an object on the surface of the planet is travelling at about 1,000 miles an hour at the equator, any object tripping such a mine would find itself flung off into space, unless acted upon by some other force. At least until it cleared the field of the mine, then our regular gravity would take over, and adjust the flight path of the object.
6a) This would include air as well, which might make for some interesting weather patterns as air leaving the planet, causing a low pressure area in the mine blast zone, high winds, etc. Interesting adventure just turning the damn thing off.
7) At present it appears that the only way to get gravity to curve space the opposite way, to turn it into a repulsive force, requires "exotic matter/energy" Which means negative mass, which is not been found and may not be findable. Not because of its non-existence, but because, well think a minute.
Start off with two masses. Identical except we flip the sign of the mass for one of them. The negative mass object, A, will be repulsed by the positive mass, B. But B is attracted to A, causing it to move closer to A. Which causes A to be pushed further from B. Right now there is no end in sight for this arraignment. B will continue to chase A, forcing it to go faster and faster, and we will see if the speed of light holds as these two objects run away from each other.
8) My own ideas of how this might be doable, shields and even warp drive, have to do with modifying the space-time manifold in a particular way. It seems to me that using constructive and destructive interference might make such devices feasable, at least in theory. Pumping energy is the same as pumping mass, and you can beam energy, with a simple radio or laser. Getting the frequencies just right, to produce the size, shape and consequences of the desired field, that might prove tricky.