Viewing the whole algebraic curve

2021 ◽  
pp. 37-53
Keyword(s):  
Algebraic Curve

On multiple curves. II

1945 ◽  
Vol 41 (2) ◽  
pp. 117-126
Author(s):  
W. V. D. Hodge
Keyword(s):  
Algebraic Curve ◽  
Abelian Integrals

In this note I consider the Abelian integrals of the first kind on an algebraic curve Γ which is a normal multiple of a curve C, as defined in Note I*.

Super Real Algebraic Curve

2004 ◽  
pp. 396-396
Author(s):  
Yolanda Lozano ◽  
Steven Duplij ◽  
Malte Henkel ◽  
Malte Henkel ◽  
Euro Spallucci ◽  
...  
Keyword(s):  
Algebraic Curve ◽  
Real Algebraic Curve

Number of points of an algebraic curve

1983 ◽  
Vol 17 (1) ◽  
pp. 53-54 ◽  
Author(s):  
S. G. Vlâdut ◽  
V. G. Drinfel'd
Keyword(s):  
Algebraic Curve

scholarly journals Moduli spaces of orthogonal and symplectic bundles over an algebraic curve

2008 ◽  
Vol 144 (3) ◽  
pp. 721-733 ◽  
Author(s):  
Olivier Serman
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Algebraic Curve ◽  
Vector Bundles ◽  
Explicit Description ◽  
Representation Space ◽  
Classical Groups ◽  
Projective Curve ◽  
Smooth Projective Curve ◽  
Polynomial Invariants

AbstractWe prove that, given a smooth projective curve C of genus g≥2, the forgetful morphism $\mathcal {M}_{\mathbf {O}_r} \longrightarrow \mathcal {M}_{\mathbf {GL}_r}$ (respectively $\mathcal M_{\mathbf {Sp}_{2r}}\longrightarrow \mathcal M_{\mathbf {GL}_{2r}}$) from the moduli space of orthogonal (respectively symplectic) bundles to the moduli space of all vector bundles over C is an embedding. Our proof relies on an explicit description of a set of generators for the polynomial invariants on the representation space of a quiver under the action of a product of classical groups.

When is a Distribution of Signs Locally Completable?

1994 ◽  
Vol 46 (3) ◽  
pp. 449-473 ◽  
Author(s):  
F. Acquistapace ◽  
F. Broglia ◽  
E. Fortuna
Keyword(s):  
Algebraic Curve ◽  
Algebraic Surface ◽  
Regular Function ◽  
Connected Components ◽  
Semialgebraic Sets ◽  
Sign Distribution

AbstractLet V be an irreducible nonsingular algebraic surface, Y ⊂ V be an algebraic curve and P a point of Y. Suppose a sign distribution is given locally in a neighbourhood of P on some connected components of V — Y. We give an algorithmic criterion to decide whether this sign distribution is induced by a regular function or not. As an application, this criterion enables one to decide whether two semialgebraic sets can be locally separated or not.

scholarly journals Faithfulness of Actions on Riemann-Roch Spaces

2015 ◽  
Vol 67 (4) ◽  
pp. 848-869 ◽  
Author(s):  
Bernhard Köck ◽  
Joseph Tait
Keyword(s):  
Finite Group ◽  
Riemann Surface ◽  
Coding Theory ◽  
Algebraic Curve ◽  
Deformation Theory ◽  
Analogous Problem ◽  
Invariant Divisor ◽  
A Finite Group

AbstractGiven a faithful action of a finite groupGon an algebraic curveXof genusgX≥ 2, we giveexplicit criteria for the induced action ofGon the Riemann–Roch spaceH0(X,OX(D)) to be faithful,whereDis aG-invariant divisor on X of degree at least 2gX− 2. This leads to a concise answer to the question of when the action ofGon the spaceH0(X,Ωx⊗m) of global holomorphic polydifferentials of order m is faithful. IfXis hyperelliptic, we provide an explicit basis of H0(X,Ωx⊗m). Finally, we giveapplications in deformation theory and in coding theory and discuss the analogous problem for theaction ofGon the first homologyH1(X,ℤ/mℤ) ifXis a Riemann surface.

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