Real Segre cubics, Igusa quartics and Kummer quartics
- Authors: Krasnov V.A.1
-
Affiliations:
- P.G. Demidov Yaroslavl State University
- Issue: Vol 84, No 3 (2020)
- Pages: 71-118
- Section: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/133808
- DOI: https://doi.org/10.4213/im8827
- ID: 133808
Cite item
Open Access
Access granted
Subscription Access
Abstract
We prove some properties of real Segre cubics. In particular, we find the topological types of the real partsof Segre cubics as well as the topological types of the real parts of the complements of the Segre planes.We prove some differential-geometric properties of the real parts of real Segre cubics and Kummer quartics.We study the automorphism groups of real Segre cubics and, in particular, their action on the real parts ofthese cubics.
About the authors
Vyacheslav Alekseevich Krasnov
P.G. Demidov Yaroslavl State University
Email: vakras@yandex.ru
Doctor of physico-mathematical sciences, Associate professor
References
- C. Segre, “Sulla varietà cubica con dieci punti doppi dello spazio a quattro dimensioni”, Atti R. Accad. Sci. Torino, XXII (1887), 791–801
- I. V. Dolgachev, Classical algebraic geometry. A modern view, Cambridge Univ. Press, Cambridge, 2012, xii+639 pp.
- B. Hunt, The geometry of some special arithmetic quotients, Lecture Notes in Math., 1637, Springer-Verlag, Berlin, 1996, xiv+332 pp.
- B. Hunt, “Nice modular varieties”, Experiment. Math., 9:4 (2000), 613–622
- В. А. Краснов, “Вещественные куммеровы квартики и их гейзенберг-инвариантность”, Изв. РАН. Сер. матем., 84:1 (2020), 105–162
- H. Finkelnberg, “Small resolutions of the Segre cubic”, Nederl. Akad. Wetensch. Indag. Math., 90:3 (1987), 261–277
- Г. Е. Шилов, Математический анализ. Функции нескольких вещественных переменных, Наука, М., 1972
- K. Rohn, “Die verschiedenen Gestalten der Kummer'schen Fläche”, Math. Ann., 18:1 (1881), 99–159
- R. W. H. T. Hudson, Kummer's quartic surface, Cambridge Univ. Press, Cambridge, 1905, xi+219 pp.
- H. F. Baker, Principles of geometry, v. 4, Cambridge Univ. Press, Cambridge, 1940, xvi+274 pp.
- M. R. Gonzalez-Dorrego, $(16,6)$ configurations and geometry of Kummer surfaces in $mathbb{P}^3$, Mem. Amer. Math. Soc., 107, no. 512, Amer. Math. Soc., Providence, RI, 1994, vi+101 pp.
- I. Nieto, “The singular $H_{2,2}$-invariant quartic surfaces in $mathbb{P}_3$”, Geom. Dedicata, 57:2 (1995), 157–170
- I. Nieto, “The normalizer of the level $(2,2)$-Heisenberg group”, Manuscripta Math., 76:3-4 (1992), 257–267
- W. Fulton, J. Harris, Representation theory. A first course, Grad. Texts in Math., 129, Springer-Verlag, New York, 1991, xvi+551 pp.
- Р. Т. Рокафеллар, Выпуклый анализ, Мир, М., 1973, 472 с.
- Göttingen collection of mathematical models and instruments
Supplementary files
