相关论文: On Translation Hyperovals in Semifield Planes
Yuzvinsky and Rose-Terao have shown that the homological dimension of the gradient ideal of the defining polynomial of a generic hyperplane arrangement is maximum possible. In this work one provides yet another proof of this result, which…
We establish half-space type results for a class of height-dependent weighted minimal surfaces in $\mathbb{R}^3$, namely critical points of a weighted area functional whose weight depends on the height. When the weight has at most quadratic…
We suggest a geometric approach to quantisation of the twisted Poisson structure underlying the dynamics of charged particles in fields of generic smooth distributions of magnetic charge, and dually of closed strings in locally…
We show that the connected sum of two copies of real projective 3-space does not admit a real projective structure. This is the first known example of a connected 3-manifold without a real projective structure.
In this paper, we prove the non-existence of certain semistable Galois representations of a number field. Our consequence can be applied to some geometric problems. For example, we prove a special case of a Conjecture of Rasmussen and…
We show that there is only one Hilbert space of entire functions that is invariant under the action of naturally defined weighted translations.
A recent preprint of S. Kojima and G. McShane [KM] observes a beautiful explicit connection between Teichm\"uller translation distance and hyperbolic volume. It relies on a key estimate which we supply here: using geometric inflexibility of…
The orientability problem in real Gromov-Witten theory is one of the fundamental hurdles to enumerating real curves. In this paper, we describe topological conditions on the target manifold which ensure that the uncompactified moduli spaces…
We provide a complete classification of groups that can be realized as isometry groups of a translation surface $M$ with non-finitely generated fundamental group and no planar ends. Furthermore, we demonstrate that if $S$ has no…
We study and report on the class of vacuum Maxwell fields in Minkowski space that possess a non-degenerate, diverging, principle null vector field (null eigenvector field of the Maxwell tensor) that is tangent to a shear-free null geodesics…
In this paper, we give the maximum of the numbers $n$ such that we can take $n$ simple closed geodesics without singularities that are disjoint to each other for translation surfaces in the hyperelliptic components $\mathcal{H}^{\rm…
We prove that a generic holomorphic foliation on a weighted projective plane has no algebraic solutions when the degree is big enough. We also prove an analogous result for foliations on Hirzebruch surfaces.
Recently, the authors of the present work (together with M. N. Kolountzakis) introduced a new version of the non-commutative Delsarte scheme and applied it to the problem of mutually unbiased bases. Here we use this method to investigate…
We prove that there is no d such that all finite projective planes can be represented by convex sets in R^d, answering a question of Alon, Kalai, Matousek, and Meshulam. Here, if P is a projective plane with lines l_1,...,l_n, a…
A plank is the part of space between two parallel planes. The following open problem, posed 45 years ago, can be viwed as the converse of Tarski's plank problem (Bang's theorem): Is it true that if the total width of a collection of planks…
Monotonicity of a mapping implies its pseudomonotonicity and hence quasimonotonocity, the converse is not true. In this note we intend to study the situations under which quasimono tonicity of a mapping implies its monotonicity. Thus we…
In this paper, we prove a monotonicity formula and some Bernstein type results for translating solitons of hypersurfaces in $\re^{n+1}$, giving some conditions under which a trantranslating soliton is a hyperplane. We also show a gap…
Consider a collection of finitely many polygons in $\mathbb C$, such that for each side of each polygon, there exists another side of some polygon in the collection (possibly the same) that is parallel and of equal length. A translation…
In this paper, we prove a theorem about embedding of some partially ordered topological spaces in topological hyperspaces equipped with Fell topology. Then we give some examples to show that the map defining the embedding may not be…
We determine the all-genus Hodge-Gromov-Witten theory of a smooth hypersurface in weighted projective space defined by a chain or loop polynomial. In particular, we obtain the first genus-zero computation of Gromov-Witten invariants for…