A brill - noether theory for k-gonal nodal curves - download pdf or read online

By Ballico E.

Show description

Read or Download A brill - noether theory for k-gonal nodal curves PDF

Best geometry and topology books

Read e-book online High Risk Scenarios and Extremes: A geometric approach PDF

Quantitative probability administration (QRM) has develop into a box of study of substantial value to varied components of program, together with coverage, banking, power, drugs, and reliability. more often than not inspired via examples from coverage and finance, the authors advance a concept for dealing with multivariate extremes.

Extra info for A brill - noether theory for k-gonal nodal curves

Example text

11. Invariant vector fields and Lie algebras. Let G be a (real) Lie group. A vector field ξ on G is called left invariant, if µ∗a ξ = ξ for all a ∈ G, where µ∗a ξ = T (µa−1 ) ◦ ξ ◦ µa as in section 3. 11) we have µ∗a [ξ, η] = [µ∗a ξ, µ∗a η], the space XL (G) of all left invariant vector fields on G is closed under the Lie bracket, so it is a sub Lie algebra of X(G). ξ(e). Thus the Lie algebra XL (G) of left invariant vector fields is linearly isomorphic to Te G, and on Te G the Lie bracket on XL (G) induces a Lie algebra structure, whose bracket is again denoted by [ , ].

Michor, 38 Chapter II. 6 −1 function theorem. a−1 = (µa ◦ ν)(x) we may conclude that ν is everywhere smooth. Xa . 4. Example. The general linear group GL(n, R) is the group of all invertible real n × n-matrices. It is an open subset of L(Rn , Rn ), given by det = 0 and a Lie group. Similarly GL(n, C), the group of invertible complex n × n-matrices, is a Lie group; also GL(n, H), the group of all invertible quaternionic n × n-matrices, is a Lie group, since it is open in the real Banach algebra LH (Hn , Hn ) as a glance at the von Neumann series shows; but the quaternionic determinant is a more subtle instrument here.

25. Theorem (local structure of singular foliations). Let E be an integrable (singular) distribution of a manifold M . Then for each x ∈ M there exists a chart (U, u) with u(U ) = {y ∈ Rm : |y i | < ε for all i} for some ε > 0, and a countable subset A ⊂ Rm−n , such that for the leaf L through x we have u(U ∩ L) = {y ∈ u(U ) : (y n+1 , . . , y m ) ∈ A}. Each leaf is an initial submanifold. If furthermore the distribution E has locally constant rank, this property holds for each leaf meeting U with the same n.

Download PDF sample

A brill - noether theory for k-gonal nodal curves by Ballico E.


by Brian
4.3

Rated 4.93 of 5 – based on 16 votes