Related papers: On Q-conic bundles, III

Our main theorem is that the pullback of an associated noncommutative vector bundle induced by an equivariant map of quantum principal bundles is a noncommutative vector bundle associated via the same finite-dimensional representation of…

We consider the internalization of the usual notion of principal bundle in a site that has all pullbacks and a terminal object. We use this notion to consider the explicit construction of quotient prestacks via presheaves of categories of…

We consider the discrete Knizhnik-Zamolodchikov connection (qKZ) associated to $gl(N)$, defined in terms of rational R-matrices. We prove that under certain resonance conditions, the qKZ connection has a non-trivial invariant subbundle…

Let X be a Fano threefold, and let S be a K3 surface in X . Any moduli space M of simple vector bundles on S carries a holomorphic symplectic structure. Following an idea of Tyurin, we show that in some cases, those vector bundles which…

We give a $K$-theoretic criterion for a quasi-projective variety to be smooth. If $\mathbb{L}$ is a line bundle corresponding to an ample invertible sheaf on $X$, it suffices that $K_q(X) = K_q(\mathbb{L})$ for all $q\le\dim(X)+1$.

In the context of non-abelian gerbes we define a cubical version of categorical group 2-bundles with connection over a smooth manifold. We define their two-dimensional parallel transport, study its properties, and define non-abelian Wilson…

We study cyclic covering morphisms from $\bar{M}_{0,n}$ to moduli spaces of unpointed stable curves of positive genus or compactified moduli spaces of principally polarized abelian varieties. Our main application is a construction of new…

Let $\pi:X\rightarrow \mathbb{P}^2$ be a K3 surface of genus 2 and $L=\pi^{\ast}\mathcal{O}_{\mathbb{P}^2}(3)$, and assume that $\pi^{\ast}\mathcal{O}_{\mathbb{P}^2}(1)$ is ample as a line bundle on $X$. In this paper, we give a numerical…

We show that any nonconstant morphism of a threefold admits a relative Chow-Kuenneth decomposition. As a corollary we get sufficient conditions for threefolds to admit an absolute Chow-Kuenneth decomposition. In case the image of the…

We show that any commutative rationally ruled surface with a choice of anticanonical curve admits a 1-parameter family of noncommutative deformations parametrized by the Jacobian of the anticanonical curve, and show that many standard facts…

A Bott manifold is a closed smooth manifold obtained as the total space of an iterated $\C P^1$-bundle starting with a point, where each $\C P^1$-bundle is the projectivization of a Whitney sum of two complex line bundles. A…

By using the classification of Fano 3-folds we prove: Let $X$ be Fano 3-fold. Assume that the tangent bundle $T_X$ of $X$ is not stable (i.e. semi-stable or unstable). Then $b_2\geq 2$ and a relative tangent sheaf $T_{X/Y}$ of a contraction…

Let $X$ be a normal projective variety defined over an algebraically closed field $k$ of positive characteristic. Let $G$ be a connected reductive group defined over $k$. We prove that some Frobenius pull back of a principal $G$-bundle…

Using a result of Longo and Xu, we show that the anomaly arising from a cyclic permutation orbifold of order 3 of a holomorphic conformal net $\mathcal A$ with central charge $c=8k$ depends on the "gravitational anomaly" $k\pmod 3$. In…

We prove that a holomorphic line bundle on a projective manifold is pseudo-effective if and only if its degree on any member of a covering family of curves is non-negative. This is a consequence of a duality statement between the cone of…

We prove that a hyperbolic Dulac germ with complex coefficients in its expansion is linearizable on a standard quadratic domain and that the linearizing coordinate is again a complex Dulac germ. The proof uses results about normal forms of…

Any ample Cartier divisor D on a projective variety X is strictly nef (i.e. D.C>0 for any effective curve C on X). In general, the converse statement does not hold. But this is conjectured to be true for anticanonical divisors. The present…

Let $\mathcal F$ be a holomorphic foliation with ample canonical bundle on a smooth projective surface $X$. We obtain an upper bound on the order of its automorphism group which depends only on $K_{\mathcal F}^2$ and $K_{\mathcal F}K_{X}$,…

For each del Pezzo surface $S$ with du Val singularities, we determine whether it admits a $(-K_S)$-polar cylinder or not. If it allows one, then we present an effective $\mathbb{Q}$-divisor $D$ that is $\mathbb{Q}$-linearly equivalent to…

It is proved by M. Paun (1997, 2017) that the fundamental group of a compact Kahler manifold X is almost Abelian if the anti-canonical bundle -KX is nef. In this paper, we apply the recent geometric analytic theory of Kahler spaces…