Related papers: On Nakayama's theorem

We generalize Iskovskih's theorem about surfaces without irregularity and bigenus from the smooth case to regular surfaces over arbitrary fields, with special focus on the case of imperfect fields. This includes surfaces that are…

In this paper, we construct derived equivalences between certain Nakayama algebras by using the notion of an S-family which is a family of objects in a triangulated category satisfying some axioms.

The aim of this fisrt part is to introduce, for a rather large class of hypersurface singularities with 1 dimensionnal locus, the analog of the Brieskorn lattice at the origin (the singular point of the singular locus). The main results are…

We study relative hypersurfaces over curves, and prove an instability condition for the fibres. This gives an upper bound on the log canonical threshold of the relative hypersurface. We compare these results with the information that can be…

An elementary proof of the two-sidedness of the matrix-inverse is given using only linear independence and the reduced row-echelon form of a matrix. In addition, it is shown that a matrix is invertible if and only if it is row-equivalent to…

For the Jacobian of a curve, the Riemann singularity theorem gives a geometric interpretation of the singularities of the theta divisor in terms of special linear series on the curve. This paper proves an analogous theorem for Prym…

In a recent paper, we stated conjectural presentations for the equivariant quantum K ring of partial flag varieties, motivated by physics considerations. In this companion paper, we analyze these presentations mathematically. We start by…

We expand our previously founded basic theory of equiresidual algebraic geometry over an arbitrary commutative field, to a well-behaved theory of (equiresidual) algebraic varieties over a commutative field, thanks to the generalisation of…

The aim of this note is to show that the "usual" proof of the Maschke Theorem in the case of a real and complex field can not be generalized at least to the case of a field of rational functions on a non-singular curve.

This paper provides a non-standard analogue of Bezout's theorem. This is acheived by showing that, in all characteristics, the notion of Zariski multiplicity coincides with intersection multiplicity when we consider the full families of…

We define smooth notions of concordance and sliceness for spatial graphs. We prove that sliceness of a spatial graph is equivalent to a condition on a set of linking numbers together with sliceness of a link associated to the graph. This…

The theorem of Mather on generic projections of smooth algebraic varieties is also proved for the singular ones.

Incidence problems between geometric objects is a key area of focus in the field of discrete geometry. Among them, the study of incidence problems over finite fields have received a considerable amount of attention in recent years. In this…

There exists a dictionary between hereditary orders and smooth stacky curves, resp. tame orders of global dimension 2 and Azumaya algebras on smooth stacky surfaces. We extend this dictionary by explaining how the restriction of a tame…

We investigate the a theorem for nonsupersymmetric gauge-Yukawa theories beyond the leading order in perturbation theory. The exploration is first performed in a model-independent manner and then applied to a specific relevant example.…

The restriction and Kakeya problems in Euclidean space have received much attention in the last few decades, and are related to many problems in harmonic analysis, PDE, and number theory. In this paper we initiate the study of these…

We prove a substantial extension of an inverse spectral theorem of Ambarzumyan, and show that it can be applied to arbitrary compact Riemannian manifolds, compact quantum graphs and finite combinatorial graphs, subject to the imposition of…

We prove, using invariant Zariski-Riemann spaces, that every normal toric variety over a valuation ring of rank one can be embedded as an open dense subset into a proper toric variety equivariantly. This extends a well known theorem of…

We consider some variations on the classical method of Runge for effectively determining integral points on certain curves. We first prove a version of Runge's theorem valid for higher-dimensional varieties, generalizing a uniform version…

In [Ann. of Math. 169 (2009)], Min Ru proved a second main theorem for algebraically nondegenerate holomorphic curves in complex projective varieties intersecting fixed hypersurface targets. In this paper, by introducing a new proof method…