Related papers: Canonical coordinates on the canonical lift

We give a differential geometric description of the Cartan (or tractor) bundle and its canonical connection in CR geometry, thus offering a direct, alternative, definition to the usual abstract approach.

Canonical extension of finitary ordered structures such as lattices, posets, proximity lattices, etc., is a certain completion which entirely describes the topological dual of the ordered structure and it does so in a purely algebraic and…

In this paper we prove the Zariski-Lipman conjecture for log canonical spaces.

We study lower bounds for the self-intersection of the canonical divisor of "canonical varieties" (i.e. varieties whose canonical linear system gives a birational map). We give some improvements for the known results in the case of surfaces…

When an endomorphism $f:X\to X$ of a projective variety which is polarized by an ample line bundle $L$, i.e. such that $f^*L\simeq L^{\otimes d}$ with $d\geq2$, is defined over a number field, Call and Silverman defined a canonical height…

A theta divisor on the universal principally polarised abelian variety can be extended to a compactification either by taking the Zariski closure, or by taking the unique extension which is pure of weight 2. For the latter, following ideas…

We determine the occurrence and explicitly describe the theta lifts on all levels of all the irreducible generic representations for the dual pair of groups $(\mathrm{Sp}_{2n}, \mathrm{O}(V))$ defined over a local nonarchimedean field…

We present an explicit construction of tilting bundles on cotangent bundles of Grassmannians of 2-planes. This construction is based on Kapranov's exceptional collection for the underlying Grassmannians, and utilizes specific iterative…

We isolate several classes of stationary sets of kappa^omega and investigate implications among them. Under a large cardinal assumption, we prove a structure theorem for stationary sets.

The log canonical thresholds of irreducible quasi-ordinary hypersurface singularities are computed, using an explicit list of pole candidates for the motivic zeta function found by the last two authors.

Let (M,I,J,K) be a compact hypercomplex manifold admitting an HKT-metric. Assume that the canonical bundle of (M,I) is trivial as a holomorphic line bundle. We show that the holonomy of Obata connection on M is contained in SL(n,H). In…

The purpose of this paper is to give two applications of Fourier transforms and generic vanishing theorems: - we give a cohomological characterization of principal polarizations - we prove that if $X$ an abelian variety and $\Theta $ a…

We prove that the cotangent bundle of a complete intersection of two general translates of the theta divisor of the jacobian of a general curve of genus 4 is ample. From this the same result for a general principally polarized abelian…

Call and Silverman introduced the canonical height associated to a polarized dynamical system, that is, an endomorphism of a projective variety and an ample line bundle which pulls back to a tensor power of itself. They also presented an…

We extend fundamental inequalities related to the canonical map of surfaces of general type to positive characteristic. Next, we classify surfaces on the Noether lines, i.e., even and odd Horikawa surfaces, in positive characteristic. We…

We prove divisorial canonicity of Fano hypersurfaces and double spaces of general position with elementary singularities.

In this paper we show that any smoothable complex projective variety, smooth in codimension two, with klt singularities and numerically trivial canonical class admits a finite cover, \'etale in codimension one, that decomposes as a product…

In this article, we will characterize the multiplier ideal sheaves with weights of log canonical threshold one by restricting the weights to complex regular surface.

We classify all the surfaces of general type whose canonical map is composed with a pencil if they are the quotient of the diagonal action by an Abelian group acting over the product of two curves. As far as we know all the previous…

A proof of the Jordan canonical form, suitable for a first course in linear algebra, is given. The proof includes the uniqueness of the number and sizes of the Jordan blocks.