All Questions

Let $P$ be a prime ideal in $S=\mathbb{C}[x_1,\ldots , x_n],$ and write $[n] = \{ 1, \ldots , n \}.$ The algebraic matroid of $P$ can be defined according to circuit axioms as follows: $C\subset [n]$ ...

If $C \subset {[n]\choose k}$ is any collection of $k$-element sets, we can define a scheme $$ W(C) = \bigcap_{S\notin C} \{V \in Gr(k,n) : p_S(V)=0\} \qquad \subseteq Gr(k,n), $$ where $p_S$ is the ...

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 ...