Fano Varieties with Many Selfmaps
نویسنده
چکیده
We study log canonical thresholds of effective divisors on weighted threedimensional Fano hypersurfaces to construct examples of Fano varieties of dimension six and higher having infinite, explicitly described, discrete groups of birational selfmaps.
منابع مشابه
Geometrical Description of Smooth Projective Symmetric Varieties with Picard Number One
In [Ru2] we have classified the smooth projective symmetric G-varieties with Picard number one (and G semisimple). In this work we give a geometrical description of such varieties. In particular, we determine their group of automorphisms. When this group, Aut(X), acts non-transitively on X, we describe a G-equivariant embedding of the variety X in a homogeneous variety (with respect to a larger...
متن کاملSmooth Projective Symmetric Varieties with Picard Number One
We classify the smooth projective symmetric G-varieties with Picard number one (and G semisimple). Moreover we prove a criterion for the smoothness of the simple (normal) symmetric varieties whose closed orbit is complete. In particular we prove that, given a such variety X which is not exceptional, then X is smooth if and only if an appropriate toric variety contained in X is smooth. keywords:...
متن کاملBirational Rigidity of Fano Varieties and Field Extensions
The modern study of the birational properties of Fano varieties started with the works of Iskovskikh; see the surveys [Isk01, Che05] and the many references there. A key concept that emerged in this area is birational rigidity. Let X be a Fano variety with Q-factorial, terminal singularities and Picard number 1. Roughly speaking, X is called birationally rigid if X can not be written in terms o...
متن کاملExplicit Examples of Birationally Rigid Fano Varieties
We construct explicit examples of divisorially canonical Fano double spaces. Their direct products are birationally rigid Fano varieties with finitely many structures of a rationally connected fiber space. 2000 Math. Subj. Class. 14E05.
متن کاملFano Hypersurfaces in Weighted Projective 4-Spaces
A Fano variety is a projective variety whose anticanonical class is ample. A 2–dimensional Fano variety is called a Del Pezzo surface. In higher dimensions, attention originally centered on smooth Fano 3–folds, but singular Fano varieties are also of considerable interest in connection with the minimal model program. The existence of Kähler–Einstein metrics on Fano varieties has also been explo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006