Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDivisor class groups of rational trinomial varieties
102
0
0.0
(
0
)
Authors
Milena Wrobel
Ask ChatGPT about the research
No Arabic abstract
We give an explicit description of the divisor class groups of rational trinomial varieties. As an application, we relate the iteration of Cox rings of any rational variety with torus action of complexity one to that of a Du Val surface.
rate research
Read More
We study finite $p$-subgroups of birational automorphism groups. By virtue of boundedness theorem of Fano varieties, we prove that there exists a constant $R(n)$ such that a rationally connected variety of dimension $n$ over an algebraically closed field is rational if its birational automorphism group contains a $p$-subgroups of maximal rank for $p > R(n)$. Some related applications on Jordan property are discussed.
In this paper we study the existence of sections of universal bundles on rational homogeneous varieties -- called nestings -- classifying them completely in the case in which the Lie algebra of the automorphism group of the variety is simple of classical type. In particular we show that, under this hypothesis, nestings do not exist unless there exists a proper algebraic subgroup of the automorphism group acting transitively on the base variety.
We prove that the divisor class group of any open Richardson variety in the Grassmannian is trivial. Our proof uses Nagatas criterion, localizing the coordinate ring at a suitable set of Plucker coordinates. We prove that these Plucker coordinates are prime elements by showing that the subscheme they define is an open subscheme of a positroid variety. Our results hold over any field and over the integers.
In this paper, we study syzygies of rational homogeneous varieties. We extend Manivels result that a $p$-th power of an ample line bundle on a flag variety satisfies Propery $(N_p)$ to many rational homogeneous varieties of type $B$, $C$, $D$, and $G_2$.
In this paper, we give an affirmative answer to a conjecture in the Minimal Model Program. We prove that log $Q$-Fano varieties of dim $n$ are rationally connected. We also study the behavior of the canonical bundles under projective morphisms.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
