Birational geometry of Fano double spaces of index two
نویسندگان
چکیده
منابع مشابه
Fano double spaces of index two
We study birational geometry of Fano varieties, realized as double covers σ: V → P M , M ≥ 5, branched over generic hypersurfaces W = W 2(M −1) of degree 2(M − 1). We prove that the only structures of a rationally connected fiber space on V are the pencils-subsystems of the free linear system | − 1 2 K V |. The groups of birational and biregular self-maps of the variety V coincide: Bir V = Aut V .
متن کاملOn the birational geometry of toric Fano 4-folds
In this Note, we announce a factorization result for equivariant birational morphisms between toric 4-folds whose source is Fano: such a morphism is always a composite of blow-ups along smooth invariant centers. Moreover, we show with a counterexample that, differently from the 3-dimensional case, even if both source and target are Fano, the intermediate varieties can not be chosen Fano. Sur la...
متن کاملBirational Unboundedness of Fano Threefolds
In this paper, we prove that the family of Fano threefolds with Picard number one is birationally unbounded.
متن کاملOn the Birational Geometry of Moduli Spaces of Pointed Curves
We prove that the moduli space Mg,n of smooth curves of genus g with n marked points is rational for g = 6 and 1 ≤ n ≤ 8, and it is unirational for g = 8 and 1 ≤ n ≤ 11, g = 10 and 1 ≤ n ≤ 3, g = 12 and n = 1. 0. Introduction and notation LetMg,n be the (coarse) moduli space of smooth curves of genus g with nmarked points defined over the field C of complex numbers and Mg,n its Deligne–Mumford ...
متن کاملBirational geometry of hypersurfaces in products of projective spaces
We study the birational properties of hypersurfaces in products of projective spaces. In the case of hypersurfaces in P × P, we describe their nef, movable and effective cones and determine when they are Mori dream spaces. Using this, we give new simple examples of non-Mori dream spaces and analogues of Mumford’s example of a strictly nef line bundle which is not ample.
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: Izvestiya: Mathematics
سال: 2010
ISSN: 1064-5632,1468-4810
DOI: 10.1070/im2010v074n05abeh002512