On the rationality of the moduli space of Lüroth quartics

Abstract

We prove that the moduli space M_L of L"uroth quartics in P^2, i.e. the space of quartics which can be circumscribed around a complete pentagon of lines modulo the action of PGL_3(CC) is rational, as is the related moduli space of Bateman seven-tuples of points in P^2.

7 pages

References in corpus (3)

• A Clebsch-Gordan formula for SL_3 and applications to rationality
• Rationality of moduli spaces of plane curves of small degree
• Rationality of the moduli spaces of plane curves of sufficiently large degree

Cited by in corpus (1)

• An explicit expression of the Luroth invariant