Automorphisms of $\mathbb{P}^1$-bundles over rational surfaces
نویسندگان
چکیده
In this paper we provide the complete classification of $\mathbb{P}^1$-bundles over smooth projective rational surfaces whose neutral component automorphism group is maximal. Our results hold any algebraically closed field characteristic zero.
منابع مشابه
Automorphisms of Finite Order on Rational Surfaces
Ž . We classify minimal pairs X, G for smooth rational projective surface X and finite group G of automorphisms on X. We also determine the fixed locus X G and the quotient surface Y X G as well as the fundamental group of the smooth part of Y. The realization of each pair is included. Mori’s extremal ray theory and recent results of Alexeev and also Ambro on the existence of good anti-canonica...
متن کاملChern Classes of Bundles on Rational Surfaces
Consider the blow up π : X̃ → X of a rational surface X at a point. Let Ṽ be a holomorphic bundle over X̃ whose restriction to the exceptional divisor isO(j)⊕O(−j) and define V = (π∗Ṽ ) . Friedman and Morgan gave the following bounds for the second Chern classes j ≤ c2(Ṽ )− c2(V ) ≤ j 2. We show that these bounds are sharp.
متن کاملAtoroidal surface bundles over surfaces
The main aim of this paper is to prove a finiteness result for atoroidal surface bundles over surfaces. It can be viewed from a number of different perspectives, and one can give several essentially equivalent statements. This, and related questions, have been considered by a number of authors. See [R] for a recent survey. First, we express it in group theoretical terms. By a surface group we m...
متن کاملCommensurability of Surface Automorphisms and surface bundles over S
Obstructions of rational commensurability of reducible surface automorphisms are given. There are 3-manifolds admitting different surface bundles structures with monodromies not rational commensurable.
متن کاملAutomorphisms of Certain Projective Bundles over Toric Varieties
The purpose of this note is to exhibit the automorphism group of a projective bundle P(E) over a simplicial toric variety X when the bundle E is a direct sum of equvariant line bundles. This case is important in the study of moduli of complete intersections on toric varieties including projective spaces. The main result is that the automorphism group of P (E) is, up to a finite group, the semi-...
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: E?pijournal de ge?ome?trie alge?brique
سال: 2023
ISSN: ['2491-6765']
DOI: https://doi.org/10.46298/epiga.2023.volume6.7603