Hyperbolic geometry and moduli of real cubic surfaces
نویسندگان
چکیده
منابع مشابه
A Complex Hyperbolic Structure for Moduli of Cubic Surfaces
We show that the moduli space M of marked cubic surfaces is biholomorphic to (B −H)/Γ0 where B is complex hyperbolic four-space, where Γ0 is a specific group generated by complex reflections, and where H is the union of reflection hyperplanes for Γ0. Thus M has a complex hyperbolic structure, i.e., an (incomplete) metric of constant holomorphic sectional curvature. Une structure hyperbolique co...
متن کاملAlgebraic surfaces and hyperbolic geometry
Many properties of a projective algebraic variety can be encoded by convex cones, such as the ample cone and the cone of curves. This is especially useful when these cones have only finitely many edges, as happens for Fano varieties. For a broader class of varieties which includes Calabi-Yau varieties and many rationally connected varieties, the Kawamata-Morrison cone conjecture predicts the st...
متن کاملExplicit Real Cubic Surfaces
The topological classification of smooth real cubic surfaces is recalled and compared to the classification in terms of the number of real lines and of real tritangent planes, as obtained by L. Schläfli in 1858. Using this, explicit examples of surfaces of every possible type are given.
متن کاملModuli spaces of surfaces and real structures
We give infinite series of groups Γ and of compact complex surfaces of general type S with fundamental group Γ such that 1) any surface S′ with the same Euler number as S, and fundamental group Γ, is diffeomorphic to S 2) the moduli space of S consists of exactly two connected components, exchanged by complex conjugation. Whence, i) on the one hand we give simple counter-examples to the DEF = D...
متن کاملModuli spaces of hyperbolic surfaces and their Weil–Petersson volumes
Moduli spaces of hyperbolic surfaces may be endowed with a symplectic structure via the Weil–Petersson form. Mirzakhani proved that Weil–Petersson volumes exhibit polynomial behaviour and that their coefficients store intersection numbers on moduli spaces of curves. In this survey article, we discuss these results as well as some consequences and applications.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales scientifiques de l'École normale supérieure
سال: 2010
ISSN: 0012-9593,1873-2151
DOI: 10.24033/asens.2116