Invariants of sets of linear varieties.
نویسنده
چکیده
A minimal set of generators of the ring of invariants for four linear subspaces of dimension n in a vector space of dimension 2n is computed, using the symbolic method introduced by Grosshans et al. [Grosshans, F., Rota, G.-C. & Stein, J. A. (1987) Invariant Theory and Superalgebras (Am. Math. Soc., Providence, RI)].
منابع مشابه
Quantum entanglement and geometry of determinantal varieties
We introduce algebraic sets, which are determinantal varieties in the complex projective spaces or the products of complex projective spaces, for the mixed states in bipartite or multipartite quantum systems as their invariants under local unitary transformations. These invariants are naturally arised from the physical consideration of measuring mixed states by separable pure states. The algebr...
متن کاملSplice Graphs and their Vertex-Degree-Based Invariants
Let G_1 and G_2 be simple connected graphs with disjoint vertex sets V(G_1) and V(G_2), respectively. For given vertices a_1in V(G_1) and a_2in V(G_2), a splice of G_1 and G_2 by vertices a_1 and a_2 is defined by identifying the vertices a_1 and a_2 in the union of G_1 and G_2. In this paper, we present exact formulas for computing some vertex-degree-based graph invariants of splice of graphs.
متن کاملBipartite Quantum Systems as an Algebraic-geometric Invariant
In [1] and [2] we defined new invariants of both bipartite and multipartite quantum systems under local unitary transformations via algebraic-geometry of determinantal varieties, and gave a new separability criterion based on our new invariants. The purpose of this note is to show how Schmidt numbers of pure states in bipartite systems, a classical invariant, can be read out from our invariants...
متن کاملAlgebraic Models, Alexander-type Invariants, and Green–lazarsfeld Sets
We relate the geometry of the resonance varieties associated to a commutative differential graded algebra model of a space to the finiteness properties of the completions of its Alexander-type invariants. We also describe in simple algebraic terms the non-translated components of the degree-one characteristic varieties for a class of non-proper complex manifolds.
متن کاملQuantum Systems as an Algebraic-geometric Invariant
In [1] and [2] we defined new invariants of both bipartite and multipartite quantum systems under local unitary transformations via algebraic-geometry of determinantal varieties, and gave a new separability criterion based on our new invariants. The purpose of this note is to show how Schmidt number of pure states in bipartite systems, a classical invariant, can be read out from algebraic-geome...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Proceedings of the National Academy of Sciences of the United States of America
دوره 87 12 شماره
صفحات -
تاریخ انتشار 1990