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Do we know any thing about cohomology of realization space of matroid (the space of all set of vectors in $\mathbb{C}^n$ which captures the independence structure of matroid $M$), more simple, for uniform matroid $U_{k,n}$? The realization space is totally determined by structure of matroid, so as the cohomology, can we write it? I found little paper about this thing, does people lost the interest to calculate it since the realization space can be vary complicated by Mnev's universal theorem?

Do we know any thing about cohomology of realization space of matroid (the space of all set of vectors in $\mathbb{C}^k$ which captures the independence structure of matroid $M$), more simple, for uniform matroid $U_{k,n}$? The realization space is totally determined by structure of matroid, so as the cohomology, can we write it? I found little paper about this thing, does people lost the interest to calculate it since the realization space can be vary complicated by Mnev's universal theorem?

Do we know any thing about cohomology of realization space of matroid (the space of all set of vectors in $\mathbb{C}^n$ which captures the independence structure of matroid $M$), more simple, for uniform matroid $U_{k,n}$? The realization space is totally determined by structure of matroid, so as the cohomology, can we write it? I found little paper about this thing, does people lost the interest to calculate it since the realiztion space can be vary complicated by Mnev's universal theorem?

Do we know any thing about cohomology of realization space of matroid (the space of all set of vectors in $\mathbb{C}^n$ which captures the independence structure of matroid $M$), more simple, for uniform matroid $U_{k,n}$? The realization space is totally determined by structure of matroid, so as the cohomology, can we write it? I found little paper about this thing, does people lost the interest to calculate it since the realization space can be vary complicated by Mnev's universal theorem?