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Accola R.D. — Topics in the Theory of Riemann Surfaces
Accola R.D. — Topics in the Theory of Riemann Surfaces

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Название: Topics in the Theory of Riemann Surfaces

Автор: Accola R.D.

Аннотация:

The book's main concern is automorphisms of Riemann surfaces, giving a foundational treatment from the point of view of Galois coverings, and treating the problem of the largest automorphism group for a Riemann surface of a given genus. In addition, the extent to which fixed points of automorphisms are generalized Weierstrass points is considered. The extremely useful inequality of Castelnuovo- Severi is also treated. While the methods are elementary, much of the material does not appear in the current texts on Riemann surfaces, algebraic curves. The book is accessible to a reader who has had an introductory course on the theory of Riemann surfaces or algebraic curves.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2008

Количество страниц: 120

Добавлена в каталог: 07.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$(\nu_1,...,\nu_s)$ group      43
$w(g^r_n, x)$, w (G, x)      17
$Z_2$      41
$\&(\Sigma)$      33
$\delta$-invariant      5
Adapted basis      13
Affine dimension of an L(D)      6
Algebraic series      21
Atlas      1
Aut(X)      1
Automorphism      1
Base points of a linear series      7
Big group      75
Biholomorphic function      1
Branched covering      36
Branching      1
Brill — Noether theorem      6
Canonical curve      9
Canonical line buncle      10
Canonical series      9
Castelnuovo’s Riemann Roch theorem      27
Cay ley representations      33
Chart      1
Clifford index      7
Clifford’s theorem      6
Clifford’s theorem, strong form      7
Commuting involutions      51
Complete linear series      7
Composite linear series      8
Compounded of an involution      9
Conformal equivalence      1
Conjugate automorphism groups      40
Cover transformation      32 37
Covering      2
Cusp      4
Cyclic coverings      54
Degree of a divisor      5
Differential, meromorphic      6
Dihedral groups      50
Divisor      5
Divisor of a differential      6
Divisor of a function      5
Elliptic function field      2
Elliptic-hyper elliptic Riemann surface      2 44
Elliptic-hyperelliptic involution      45
Equivalent coverings      30
Equivalent divisors      5
Equivalent line bundles      11
Expected weight      71
Extraordinary gap      18
Extraordinary non-gap      18
Fixed points of a linear series      7
Flex      18
Function fields      2
G(Y/X)      32
G-weight      59
Galois closure      36
Galois group      32 34
Gap      17
Generalized Weierstrass point      17
Greatest common divisor      5
Groups of genus one      44
Groups of genus zero      43
Groups with partitions      48
Higher order Weierstrass point      17
Holomorphic differential      6
Holomorphic function      1
Holomorphic section      11
Hyperelliptic involution      2
Hyperelliptic Riemann surface      2
Imposing linear conditions      10
Incomplete linear series      7
Index of speciality      6
Inequality of Castelnuovo — Severi      21
Integral divisor      5
Inverse line bundle      12
Involution (automorphism)      1
Involution of genus q      8
k-canonical line bundle      12
kK points      53
L(D)      5
Lift      30
Line bundle      10
Linear series      7
Linear series invariant under a group      64
Local parameter      1
m(X)      2
M(Y/X)      35
Maximal automorphism groups      45
Meromorphic function      1
Monodromy group of a covering      35
Monodromy theorem      30
Multiplicity of branching      1
N(p)      42
Node      4
Non-gap      17
Normal covering      34
Number of sheets      1
o(f)      2
Ordinary singularity      4
Plane curve      3
Plane model      9
Positive divisor      5
Product of line bundles      12
Projective dimension of L(D)      6
Ramification      1
Rational function field      2
Regular permutation group      33
Riemann surface      1
Riemann-Hurwitz formula for coverings      2
Riemann-Hurwitz formula for Galois coverings      38
Riemarin — Roch theorem      6
Section      11
Simple linear series      8
Singularities of plane curves      4
Smooth covering      30
Special divisor      6
surface      1
Tacnode      4
Transition function      10
Transitive permutation group      33
Type I, II, III groups      77
Uniformization theorem      31
Universal covering      31
w(G, A)      71
Weierstrass point      13
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