Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userManifolds with two projective bundle structures
231
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this paper we classify varieties of Picard number two having two projective bundle structures of any relative dimension, under the assumption that these structures are mutually uniform. As an application we prove the Campana--Peternell conjecture for varieties of Picard number one admitting $mathbb C^*$-actions of a certain kind.
rate research
Read More
We study the branched holomorphic projective structures on a compact Riemann surface $X$ with a fixed branching divisor $S, =, sum_{i=1}^d x_i$, where $x_i ,in, X$ are distinct points. After defining branched ${rm SO}(3,{mathbb C})$--opers, we show that the branched holomorphic projective structures on $X$ are in a natural bijection with the branched ${rm SO}(3,{mathbb C})$--opers singular at $S$. It is deduced that the branched holomorphic projective structures on $X$ are also identified with a subset of the space of all logarithmic connections on $J^2((TX)otimes {mathcal O}_X(S))$ singular over $S$, satisfying certain natural geometric conditions.
For a Lagrangian torus A in a simply-connected projective symplectic manifold M, we prove that M has a hypersurface disjoint from a deformation of A. This implies that a Lagrangian torus in a compact hyperkahler manifold is a fiber of an almost holomorphic Lagrangian fibration, giving an affirmative answer to a question of Beauvilles. Our proof employs two different tools: the theory of action-angle variables for algebraically completely integrable Hamiltonian systems and Wielandts theory of subnormal subgroups.
Let $X$ be a nonsingular projective $n$-fold $(nge 2)$ of Fano or of general type with ample canonical bundle $K_X$ over an algebraic closed field $kappa$ of any characteristic. We produce a new method to give a bunch of inequalities in terms of all the Chern classes $c_1, c_2, cdots, c_n$ by pulling back Schubert classes in the Chow group of Grassmannian under the Gauss map. Moreover, we show that if the characteristic of $kappa$ is $0$, then the Chern ratios $(frac{c_{2,1^{n-2}}}{c_{1^n}}, frac{c_{2,2,1^{n-4}}}{c_{1^n}}, cdots, frac{c_{n}}{c_{1^n}})$ are contained in a convex polyhedron for all $X$. So we give an affirmative answer to a generalized open question, that whether the region described by the Chern ratios is bounded, posted by Hunt (cite{Hun}) to all dimensions. As a corollary, we can get that there exist constants $d_1$, $d_2$, $d_3$ and $d_4$ depending only on $n$ such that $d_1K_X^nlechi_{top}(X)le d_2 K_X^n$ and $d_3K_X^nlechi(X, mathscr{O}_X)le d_4 K_X^n$. If the characteristic of $kappa$ is positive, $K_X$ (or $-K_X$) is ample and $mathscr{O}_X(K_X)$ ($mathscr{O}_X(-K_X)$, respectively) is globally generated, then the same results hold.
Geometric structures on manifolds became popular when Thurston used them in his work on the geometrization conjecture. They were studied by many people and they play an important role in higher Teichmuller theory. Geometric structures on a manifold are closely related with representations of the fundamental group and with flat bundles. Higgs bundles can be very useful in describing flat bundles explicitly, via solutions of Hitchins equations. Baraglia has shown in his Ph.D. Thesis that Higgs bundles can also be used to construct geometric structures in some interesting cases. In this paper, we will explain the main ideas behind this theory and we will survey some recent results in this direction, which are joint work with Qiongling Li.
We establish a formula for computing the unramified Brauer group of tame conic bundle threefolds in characteristic 2. The formula depends on the arrangement and residue double covers of the discriminant components, the latter being governed by Artin-Schreier theory (instead of Kummer theory in characteristic not 2). We use this to give new examples of threefold conic bundles defined over the integers that are not stably rational over the complex numbers.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
