Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHigh rank torus actions on contact manifolds
85
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We prove LeBrun--Salamon conjecture in the following situation: if $X$ is a contact Fano manifold of dimension $2n+1$ whose group of automorphisms is reductive of rank $geq max(2,(n-3)/2)$ then $X$ is the adjoint variety of a simple group. The rank assumption is fulfilled not only by the three series of classical linear groups but also by almost all the exceptional ones.
rate research
Read More
We extend the Altmann-Hausen presentation of normal affine algebraic C-varieties endowed with effective torus actions to the real setting. In particular, we focus on actions of quasi-split real tori, in which case we obtain a simpler presentation.
We show that joinings of higher rank torus actions on S-arithmetic quotients of semi-simple or perfect algebraic groups must be algebraic.
We show that no torus knot of type $(2,n)$, $n>3$ odd, can be obtained from a polynomial embedding $t mapsto (f(t), g(t), h(t))$ where $(deg(f),deg(g))leq (3,n+1) $. Eventually, we give explicit examples with minimal lexicographic degree.
We compute the motive of the variety of representations of the torus knot of type (m,n) into the affine groups $AGL_1(C)$ and $AGL_2(C)$. For this, we stratify the varieties and show that the motives lie in the subring generated by the Lefschetz motive q=[C].
For complete intersection Calabi-Yau manifolds in toric varieties, Gross and Haase-Zharkov have given a conjectural combinatorial description of the special Lagrangian torus fibrations whose existence was predicted by Strominger, Yau and Zaslow. We present a geometric version of this construction, generalizing an earlier conjecture of the first author.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
