Bitangent of quartic
WebJun 1, 2011 · The theory of plane quartic curves is a delightful chapter of 19th century mathematics, with contributions by Aronhold, Cayley, Frobenius, Hesse, Klein, Schottky, … WebJSTOR Home
Bitangent of quartic
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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 ... Indeed, 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 ... 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 …
WebMar 24, 2024 · A bitangent is a line that is tangent to a curve at two distinct points. Aa general plane quartic curve has 28 bitangents in the complex projective plane. However, as shown by Plücker (1839), the … WebSuperabundance phenomena in tropical geometry pose a challenge to addressing enumerative geometry questions by combinatorial means [4, 29, 36, 37].For example, smooth tropical plane quartic curves can have infinitely many bitangent tropical lines, as opposed to the count of 28 bitangents to smooth algebraic plane quartic curves over …
WebSep 17, 2014 · Abstract:Aronhold's classical result states that a plane quartic can be recovered bythe configuration of any Aronhold systems of bitangents, i.e. special 7 … 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.
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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 ... song go insane by lindsey buckinghamWebG\: 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 song gold by john stewart and stevie nicksWebMar 17, 2024 · Aronhold’s classical result states that a plane quartic can be recovered by the configuration of any Aronhold systems of bitangents, i.e., special 7-tuples of … song gold by john stewartWebMar 25, 2024 · Any odd theta-characteristic can be represented by an effective divisor. When $C$ is a plane quartic (so $g = 3$) such a divisor has form $P_1 + P_2$, and the … song goldfishWeb1 day ago · The tropical bitangent classes to a smooth tropical quartic curve Γ are the connected components in R 2 consisting of all the vertices of tropical bitangents in the … song golden brown by the stranglershttp://www-personal.umich.edu/~kailasas/quart28-fin.pdf smaller keyboard win 10WebIn 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 … song golden years david bowie