Related papers: Maximal rank for planar singularities of multiplic…

We generalise the proof by Marian and Oprea of rank-level duality for non-abelian theta functions to the case of sections of line bundles (conformal blocks) over moduli spaces of parabolic vector bundles over a projective smooth curve. We…

In this paper we investigate Abel maps on normal surface singularities described in \cite{NNI}. We investigate the affine version of the class of the images of Abel maps on normal surface singularities. More precisely we consider the…

A notion of open rank, related with generic power sum decompositions of forms, has recently been introduced in the literature. The main result here is that the maximum open rank for plane quartics is eight. In particular, this gives the…

We show that the algebraic boundaries of the regions of real binary forms with fixed typical rank are always unions of dual varieties to suitable coincident root loci.

We prove a general dichotomy theorem for groups of finite Morley rank with solvable local subgroups and of Pr\"ufer p-rank at least 2, leading either to some p-strong embedding, or to the Pr\"ufer p-rank being exactly 2.

We prove a generalization of a result of Peres and Schlag on the dimensions of certain exceptional sets of projections and then apply it to a geometric problem.

For a smooth projective toric variety of Picard rank two we classify all exceptional sequences of invertible sheaves which have maximal length. In particular, we prove that unlike non-maximal sequences, they (a) remain exceptional under…

We prove the existence of a genus-zero complete maximal map with a prescribed singularity set and an arbitrary number of simple and complete ends. We also discuss the conditions under which this maximal map can be made into a complete…

Each irreducible representation of the motion group of the plane has a unique maximal inductive algebra, and it is self adjoint.

We generalize the existence of maximal orders in a semi-simple algebra for general ground rings. We also improve several statements in Chapter 5 and 6 of Reiner's book concerning separable algebras by removing the separability condition,…

In this paper we count the number of some particular quadruple persymmetric rank i matrices over F_2.

We argue that the spiral can, in presence of a maximum principle, be of maximal rank at a boundary, but does not preserve hypoellipticity.

We construct a non-full exceptional collection of maximal length consisting of line bundles on the blow-up of the projective plane in 10 points in general position. This provides a counterexample to a conjecture of Kuznetsov and to a…

Let $r$ and $n$ be positive integers such that $r<n$, and $\mathbb{K}$ be an arbitrary field. In a recent work, we have determined the maximal dimension for a linear subspace of $n$ by $n$ symmetric matrices with rank less than or equal to…

Building on our earlier results on tropical independence and shapes of divisors in tropical linear series, we give a tropical proof of the maximal rank conjecture for quadrics. We also prove a tropical analogue of Max Noether's theorem on…

We address the following question: what are the cardinalities of maximal finite families of pairwise incident planes in a complex projective space? One proves easily that the span of the planes has dimension 5 or 6. Up to projectivities…

We find an invariant characterization of planar webs of maximum rank. For 4-webs, we prove that a planar 4-web is of maximum rank three if and only if it is linearizable and its curvature vanishes. This result leads to the direct…

We study an upper bound of ranks of $n$-tensors with size $2\times\cdots\times2$ over the complex and real number field. We characterize a $2\times 2\times 2$ tensor with rank 3 by using the Cayley's hyperdeterminant and some function. Then…

We prove that affine maps are uniquely extremal quasiconformal maps on the complement of a well distribute set in the complex plane answering a conjecture from \cite{markovic}. We construct the required Reich sequence using Bergman…

A rank-$r$ integer matrix $A$ is $\Delta$-modular if the determinant of each $r \times r$ submatrix has absolute value at most $\Delta$. The class of $1$-modular, or unimodular, matrices is of fundamental significance in both integer…