相关论文: Surface Bundles With Non-Zero Signature
We obtain sufficient conditions exlcuding the existence of non-trivial distribution sections of bundles over the boundary of symmetric spaces of negative curvature which are invariant with respect to a geometrically finite group of…
This paper is a continuation of arXiv:1205.4415. We focus on non-K3 surfaces providing some improvements of known results.
Werner Meyer constructed a cocycle in $H^2(Sp(2g, \mathbb{Z}); \mathbb{Z})$ which computes the signature of a closed oriented surface bundle over a surface, with fibre a surface of genus g. By studying properties of this cocycle, he also…
We give the classification of globally generated vector bundles of rank $2$ on a smooth quadric surface with $c_1\le (2,2)$ in terms of the indices of the bundles, and extend the result to arbitrary higher rank case. We also investigate…
We explain how the current knowledge on the set of complete noncompact constant mean curvature surfaces can be exploited to produce new examples of compact constant mean curvature surfaces of genus greater than or equal to 3.
The article proves the Infinitesimal Torelli theorem for surfaces subject to the following conditions: 1) the canonical bundle of a surface is ample and generated by its global sections, 2)the geometric genus $p_g \geq 4$, 3) the…
We construct infinitely many distinct hypersurfaces with prescribed mean curvature (PMC) for a large class of prescribing functions when $(M^{n+1}, g)$ is a closed smooth manifold containing a minimal surface that is strictly stable (or…
End sum is a natural operation for combining two noncompact manifolds and has been used to construct various manifolds with interesting properties. The uniqueness of end sum has been well-studied in dimensions three and higher. We study end…
We present a simple algorithm for differentiable rendering of surfaces represented by Signed Distance Fields (SDF), which makes it easy to integrate rendering into gradient-based optimization pipelines. To tackle visibility-related…
We use hypersurfaces containing unexpected linear spaces to construct interesting vector bundles on complete intersection surfaces in projective space. We discover examples of moduli spaces of rank 2 stable bundles on surfaces of Picard…
In the present note we describe geometrically the homology classes in the total space of a surface bundle over a surface in terms of the holonomy map. We treat the cases where the base surface is closed or has one boundary component. We…
The signature is an infinite graded sequence of statistics known to characterise a stream of data up to a negligible equivalence class. It is a transform which has previously been treated as a fixed feature transformation, on top of which a…
We introduce a new method to study mixed characteristic deformation of line bundles. In particular, for sufficiently large smooth projective families $f : \mathscr{X} \to \mathscr{S}$ defined over the ring of $N$-integers…
We introduce Topological Offsets, a novel approach to generate manifold and self-intersection-free offset surfaces that are topologically equivalent to an offset infinitesimally close to the surface. Our approach, by construction, creates a…
In this article we study asymptotic slopes of strongly semistable vector bundles on a smooth projective surface. A connection between asymptotic slopes and strong restriction theorem of a strongly semistable vector bundle is shown. We also…
Let $S$ be a surface with $p_g(S)=q(S)=0$ and endowed with a very ample line bundle $\mathcal O_S(h)$ such that $h^1\big(S,\mathcal O_S(h)\big)=0$. We show that $S$ supports special (often stable) Ulrich bundles of rank $2$, extending a…
This paper is concerned with projective rationally connected surfaces $X$ with canonical singularities and having non-zero pluri-forms, i.e. $(\Omega_X^1)^{[\otimes m]}$ has non-zero global sections for some m > 0, where…
In this paper, an upper bound on the nullity of signed graphs in terms of the cyclomatic number and the number of pendant vertices is proved, and the corresponding extremal signed graphs are completely characterized.
One of the most efficient ways to produce unconditional simulations is with the spectral method using fast Fourier transform (FFT) [1]. But this approach is not applicable to arbitrary surfaces because no regular grid exists. However,…
We characterize property $(N_p)$ on a polarized surface $(X,L)$ with trivial canonical bundle in terms of the (non)existence of certain forbidden subvarieties of $X$.