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Recovery of Plane Curves from Branch Points
We recover plane curves from their branch points under projection onto a line. Our focus lies on cubics and quartics. These have 6 and 12 branch...
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Braid monodromy and Alexander polynomials of real plane curves
We describe symmetries of the braid monodromy decomposition for a class of plane curves defined over reals including the real curves with no real...
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Classification of unstable quartic plane curves
Consider the action by change of coordinates in the space of quartic plane curves. We classify the unstable points of this action through a...
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On smooth plane models for modular curves of Shimura type
In this paper we prove that there are finitely many modular curves that admit a smooth plane model. Moreover, if the degree of the model is greater...
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Remarks on double points of plane curves
We study the relation between the type of a double point of a plane curve and the curvilinear 0-dimensional subschemes of the curve at the point. An...
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Equi-affine plane curves with singular points
We deal with not only regular equi-affine plane curves with inflection points but also singular equi-affine plane curves (equi-affine plane curves...
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Curves in the Plane
The simplest object of differential geometry is a curve in the plane. The definition of a curve varies between different areas of mathematics. In...
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Normal surface singularities with an integral homology sphere link related to space monomial curves with a plane semigroup
In this article, we consider an infinite family of normal surface singularities with an integral homology sphere link which is related to the family...
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Plane Algebraic Curves with Prescribed Singularities
We give a survey on the known results about the problem of the existence of complex and real algebraic curves in the plane with prescribed...
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Bi-Lipschitz Characterization of Space Curves
In the paper Targino (Outer Lipschitz Geometry of Complex Algebraic Plane Curves. International Mathematics Research Notices, rnac202.
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Real Algebraic Geometry of Real Algebraic Jordan Curves in the Plane and the Bergman Kernel
We characterize the space of restrictions of real rational functions to certain algebraic Jordan curves in the plane via the Dirichlet-to-Neumann map...
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Terracini loci of curves
We study subsets S of curves X whose double structure does not impose independent conditions to a linear series L , but there are divisors
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A Non-standard Bezout Theorem for Curves
This paper provides a non-standard analogue of Bezout’s theorem for algebraic curves. We achieve this by showing that, in all characteristics, the...
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On Vertices of Frontals in the Euclidean Plane
We investigate vertices for plane curves with singular points. As plane curves with singular points, we consider Legendre curves (respectively,...
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Parametrizations and Plane Curves
The chapter is devoted to the study of plane curves from the point of view of differential geometry. We focus our attention to classical curves and...
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Elliptic Curves over the Rationals
This chapter covers prerequisites on elliptic curves over $$\mathbb...
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