http://www-personal.umich.edu/~kailasas/quart28-fin.pdf WebG\: the general plane quartic is a G\], 2. A plane quartic curve has in general 28 bitangents. An infinite number of conies touch the curve at four separate points, and certain of these conies break up into two bitangent lines: it is scarcely possible to discuss the bitangents apart from the conies. It

A tropical count of real bitangents to plane quartic curves

An explicit quartic with twenty-eight real bitangents was first given by Plücker As Plücker showed, the number of real bitangents of any quartic must be 28, 16, or a number less than 9. Another quartic with 28 real bitangents can be formed by the locus of centers of ellipses with fixed axis lengths, tangent to two … See more In the theory of algebraic plane curves, a general quartic plane curve has 28 bitangent lines, lines that are tangent to the curve in two places. These lines exist in the complex projective plane, but it is possible to define … See more The Trott curve, another curve with 28 real bitangents, is the set of points (x,y) satisfying the degree four polynomial equation See more 1. ^ See e.g. Gray (1982). 2. ^ Blum & Guinand (1964). 3. ^ Trott (1997). 4. ^ Riemann (1876); Cayley (1879). 5. ^ Manivel (2006). See more The dual curve to a quartic curve has 28 real ordinary double points, dual to the 28 bitangents of the primal curve. The 28 bitangents of a quartic may also be placed in correspondence with symbols of the form See more WebIt is well known [Pl] that a nonsingular plane quartic curve C over an algebraically closed field of characteristic 2 has exactly 28 bitangents. The same is still true if ... in this case, there is a rational bitangent. One may start with a cubic surface with the right Galois operation [EJ15], blow-up a rational point, and use the connection ... earl slick tour dates

A TROPICAL COUNT OF REAL BITANGENTS TO PLANE …

WebMay 6, 2024 · 28 bitangent lines to sm. plane quartics over K=C((t)). Theorem:There are 28 classical bitangents to sm. plane quartics over K but 7 tropical bitangent classes to their smooth tropicalizations in R2. Trop. sm. quartic=dual to unimodular triangulation of 2 of side length 4. duality gives agenus 3 planar metric graph. WebA bitangent differs from a secant line in that a secant line may cross the curve at the two points it intersects it. One can also consider bitangents that are not lines; for … WebDec 8, 2024 · A smooth tropical quartic curve has seven tropical bitangent classes. Their shapes can vary within the same combinatorial type of curve. We study deformations of these shapes and we show that the ... earl slick guitars