Displaying similar documents to “Optimal degree construction of real algebraic plane nodal curves with prescribed topology. I. The orientable case.”

A really elementary proof of real Lüroth's theorem.

T. Recio, J. R. Sendra (1997)

Revista Matemática de la Universidad Complutense de Madrid

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Classical Lüroth theorem states that every subfield K of K(t), where t is a transcendental element over K, such that K strictly contains K, must be K = K(h(t)), for some non constant element h(t) in K(t). Therefore, K is K-isomorphic to K(t). This result can be proved with elementary algebraic techniques, and therefore it is usually included in basic courses on field theory or algebraic curves. In this paper we study the validity of this result under weaker assumptions: namely, if K...

Curves in P(C) with 1-dimensional symmetry.

A. A. du Plessis, Charles Terence Clegg Wall (1999)

Revista Matemática Complutense

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In a previous paper we showed that the existence of a 1-parameter symmetry group of a hypersurface X in projective space was equivalent to failure of versality of a certain unfolding. Here we study in detail (reduced) plane curves of degree d ≥ 3, excluding the trivial case of cones. We enumerate all possible group actions -these have to be either semisimple or unipotent- for any degree d. A 2-parameter group can only occur if d = 3. Explicit lists of singularities of the corresponding...

On the Difference of 4-Gonal Linear Systems on some Curves

Ohbuchi, Akira (1997)

Serdica Mathematical Journal

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Let C = (C, g^1/4 ) be a tetragonal curve. We consider the scrollar invariants e1 , e2 , e3 of g^1/4 . We prove that if W^1/4 (C) is a non-singular variety, then every g^1/4 ∈ W^1/4 (C) has the same scrollar invariants.