Segre quartic surfaces and minitwistor spaces

Autor:	Honda, Nobuhiro
Rok vydání:	2020
Předmět:	Mathematics - Algebraic Geometry Mathematics - Differential Geometry
Druh dokumentu:	Working Paper
Popis:	Segre surfaces in the title mean quartic surfaces in $\mathbb{CP}^4$ which are the images of weak del Pezzo surfaces of degree four under the anti-canonical map. We first show that minimal minitwistor spaces with genus one are exactly Segre quartic surfaces. By a kind of Penrose correspondence, Zariski open subsets of the projective dual varieties of these surfaces admit Einstein-Weyl structure. We investigate structures of these dual varieties in detail. In particular, we determine the degrees of these varieties (namely the classes of the Segre surfaces), as well as structure of several components of the boundary divisors which are the complements of the Einstein-Weyl spaces in the projective dual varieties. Comment: 38 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2009.05242 Zobrazit plný text záznamu View this record from Arxiv