Explicit computations of invariants of plane quartic curves
نویسنده
چکیده
We establish a complete set of invariants for ternary quartic forms. Further, we express four classical invariants in terms of these generators.
منابع مشابه
TENSION QUARTIC TRIGONOMETRIC BÉZIER CURVES PRESERVING INTERPOLATION CURVES SHAPE
In this paper simple quartic trigonometric polynomial blending functions, with a tensionparameter, are presented. These type of functions are useful for constructing trigonometricB´ezier curves and surfaces, they can be applied to construct continuous shape preservinginterpolation spline curves with shape parameters. To better visualize objects and graphics atension parameter is included. In th...
متن کاملA descent method for explicit computations on curves
It is shown that the knowledge of a surjective morphism $Xto Y$ of complex curves can be effectively used to make explicit calculations. The method is demonstrated by the calculation of $j(ntau)$ (for some small $n$) in terms of $j(tau)$ for the elliptic curve with period lattice $(1,tau)$, the period matrix for the Jacobian of a family of genus-$2$ curves complementing the classi...
متن کاملNon-hyperelliptic curves of genus three over finite fields of characteristic two
Let k be a finite field of even characteristic. We obtain in this paper a complete classification, up to k-isomorphism, of non singular quartic plane curves defined over k. We find explicit rational normal models and we give closed formulas for the total number of k-isomorphism classes. We deduce from these computations the number of k-rational points of the different strata by the Newton polyg...
متن کاملModuli of Plane Quartics, Göpel Invariants and Borcherds Products
ABSTRACT. It is known that the moduli space of plane quartic curves is birational to an arithmetic quotient of a 6-dimensional complex ball ([Kon1]). In this paper, we shall show that there exists a 15-dimensional space of meromorphic automorphic forms on the complex ball which gives a birational embedding of the moduli space of plane quartics with level 2 structure into P. This map coincides w...
متن کاملClassification of Genus 3 Curves in Special Strata of the Moduli Space
We describe the invariants of plane quartic curves — nonhyperelliptic genus 3 curves in their canonical model — as determined by Dixmier and Ohno, with application to the classification of curves with given structure. In particular, we determine modular equations for the strata in the moduli spaceM3 of plane quartics which have at least seven hyperflexes, and obtain an computational characteriz...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Symb. Comput.
دوره 68 شماره
صفحات -
تاریخ انتشار 2015