The Hesse pencil of plane cubic curves

By M. Artebani, Igor Dolgachev. 2006

141 citations recorded by the source corpus.

This is a survey of the classical geometry of the Hesse configuration of 12 lines in the projective plane related to inflection points of a plane cubic curve. We also study two K3 surfaces with Picard number 20 which arise naturally in connection with the configuration.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/3d3b97ddfab67cdda84643e52bc815a37d2136c6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Giancarlo Urzúa
2. Igor Dolgachev

In Computational Theory and Mathematics

1. Giancarlo Urzúa
2. Igor Dolgachev
3. D. Huybrechts

In Geometry and Topology

1. Giancarlo Urzúa
2. Igor Dolgachev
3. Serge Cantat
4. Carlos Simpson
5. D. Huybrechts

Citations in the corpus

• Classical Algebraic Geometry: A Modern View (2012, background): “44) U1 − U5 = 6[15, 46, 23], U1 − U6 = 6[16, 25, 34], U2 − U3 = 6[15, 26, 34], U2 − U4 = 6[13, 46, 25], U2 − U5 = 6[16, 35, 24], U2 − U6 = 6[14, 23, 56], U3 − U4 = 6[16, 45, 23], U3 − U5 = 6[14, 25, 36], U3 − U6 = 6[12, 46, 35], U4 − U5 = 6[12, 43, 56], U4 − U6 = 6[15, 36, 24], U5 − U6 = 6[13, 45, 2”
• Arrangements of curves and algebraic surfaces (2007, background): “The rest of the points in X ′ (again, although A′ is not a net, we think of X ′ as the set of 3-points inA′ coming from X ) [[1, 3, 6]] and [[2, 4, 5]] give the same restriction (a− 1)(b− 1) = 1, i.”