부산대학교 도서관

This paper is a sequel to [Part I, J. Kosakowska and M. Schmidmeier, Trans. Amer. Math. Soc. {\bf 367} (2015), no.~8, 5475--5505; MR3347180]. For a partition $\alpha$ (a finite non-increasing sequence of non-negative integers) denote by $N_{\alpha}$ the finite-dimensional module over the polynomial algebra $k[T]$ on which $T$ acts as a nilpotent linear operator of Jordan type $\alpha$ ($k$ is an algebraically closed field). Fix partitions $\beta,\gamma$ with $b=|\beta|>|\gamma|=b-a$. The category of short exact sequences $0\to N_{\alpha}\to N_{\beta}\to N_{\gamma}\to 0$ contains a full subcategory $\Cal{S}$ whose objects are short exact sequences as above with $\alpha_1\le 2$ (equivalently, $T^2$ annihilates $N_{\alpha}$). There is an affine variety $\Bbb{V}$ endowed with an action of $G\coloneq GL_a(k)\times GL_b(k)$ whose points parametrize objects from $\Cal{S}$ in such a way that the $G$-orbits are in bijection with the isomorphism classes. To an isomorphism class in $\Cal{S}$ the authors assign a combinatorial object, a so-called {\it arc diagram}. Now the variety $\Bbb{V}$ is stratified as the disjoint union of its $G$-invariant locally closed subsets consisting of points corresponding to an isomorphism class with a given arc diagram. The authors compute the dimension of each stratum, and describe in terms of the combinatorics of arc diagrams which strata lie on the Zariski closure of a given stratum.