On Rationality of Nonsingular Threefolds with a Pencil of Del Pezzo Surfaces of Degree 4
نویسنده
چکیده
We prove a criterion of nonsingularity of a complete intersection of two fiberwise quadrics in P P 1 (O(d 1) ⊕. .. ⊕ O(d 5)). As a corollary we derive the following addition to the Alexeev theorem on rationality of standard Del Pezzo fibrations of degree 4 over P 1 : we prove that any fibration of this kind with the topological Euler characteristic χ(X) = −4 is rational.
منابع مشابه
Extremal Metrics on Del Pezzo Threefolds
X iv :0 81 0. 19 24 v3 [ m at h. A G ] 7 F eb 2 00 9 EXTREMAL METRICS ON DEL PEZZO THREEFOLDS IVAN CHELTSOV AND CONSTANTIN SHRAMOV In memory of Vasily Iskovskikh Abstract. We prove the existence of Kähler–Einstein metrics on a nonsingular section of the Grassmannian Gr(2, 5) ⊂ P by a linear subspace of codimension 3, and the Fermat hypersurface of degree 6 in P(1, 1, 1, 2, 3). We also show that...
متن کاملBirational Maps of Del Pezzo Fibrations
In classical result, it is known that any P-bundle over a nonsingular curve T can be birationally transformed to P-bundle over a nonsingular curve T by an elementary transformation. Here, we can ask if it is also possible in 3-fold case. In other words, is it true that any nonsingular del Pezzo fibration over a nonsingular curve can be transformed to another nonsingular del Pezzo fibration? In ...
متن کاملWeak Del Pezzo Surfaces with Irregularity
I construct normal del Pezzo surfaces, and regular weak del Pezzo surfaces as well, with positive irregularity q > 0. This can happen only over nonperfect fields. The surfaces in question are twisted forms of nonnormal del Pezzo surfaces, which were classified by Reid. The twisting is with respect to the flat topology and infinitesimal group scheme actions. The twisted surfaces appear as generi...
متن کاملWeak Del Pezzo with Irregularity
I construct normal del Pezzo surfaces, and regular weak del Pezzo surfaces as well, with positive irregularity q > 0. Such things can happen only over nonperfect fields. The surfaces in question are twisted forms of nonnormal del Pezzo surfaces, which were classified by Reid. The twisting is with respect to the flat topology and infinitesimal group scheme actions. The twisted surfaces appear as...
متن کاملThreefolds whose canonical bundles are not numerically effective.
Let X be an arbitrary nonsingular projective 3-fold whose canonical bundle is not numerically effective. Then we have: (i) X contains an exceptional divisor of several types, which we classify explicitly, (ii) X has a morphism to a projective nonsingular surface whose fibers are conics, (iii) X has a morphism to a projective nonsingular curve whose general fibers are Del Pezzo surfaces, or (iv)...
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 2007