Recovering plane curves from their bitangents
By Lucia Caporaso, E. Sernesi. 2000
58 citations recorded by the source corpus.
We show that a general plane curve of degree at least 4 is uniquely determined by the full set of its bitangent lines. This problem has an elementary solution for degree at least 5, and the paper is almost entirely devoted to curves of degree 4, where we generalize the result to nodal quartics. In other words, we show that a general curve of genus 3 can be recovered from its 28 odd theta-characteristics.
View Paper: https://www.semanticscholar.org/paper/d2f3ad571c147a6b14a53a5eb8dc45856870d41f
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
- G. Farkas
- R. Pandharipande
- Igor Dolgachev
- Davesh Maulik
- A. Okounkov
- Dawei Chen
- Ingrid Bauer
- Yukinobu Toda
Citations in the corpus
- Classical Algebraic Geometry: A Modern View (2012, background): “Only recently it was proven that the answer is yes: [62] (for a general curve), [357] (for any nonsingular curve).”
- Topics in classical algebraic geometry (2006, background): “Only recently it was proven that the answer is yes: [31] (for general curve), [189] (for any nonsingular curve).”
- THE MODULI SPACE OF TWISTED CANONICAL DIVISORS (2015, background): “A general quartic C ⊂ P(2) can be reconstructed from its 28 bitangent lines [3]: the rational map M3 99K Sym28(P2)∨//PGL(3) , C 7→ θ(C) is generically injective.”