Related papers: On singular varieties having an extremal secant li…

We investigate full strongly exceptional collections on smooth, com- plete toric varieties. We obtain explicit results for a large family of varieties with Picard number three, containing many of the families already known. We also describe…

In this paper we consider ideal sheaves associated to the singular loci of a divisor in a linear system $|L|$ of an ample line bundle on a complex abelian variety. We prove an effective result on their (continuous) global generation, after…

This paper has been withdrawn by the author due to a crucial error.

We introduce and study a new way to catagorize supersingular abelian varieties defined over a finite field by classifying them as fully maximal, mixed, or fully minimal. The type of $A$ depends on the normalized Weil numbers of $A$ and its…

A variety of minimal degree is one of the basic objects in projective algebraic geometry and has been classified and characterized in many aspects. On the other hand, there are also minimal objects in the category of higher secant…

We show that generic vanishing fails for singular varieties and in characteristic p>0.

Building on previous work of Kollar, Ein, Lazarsfeld, and Hacon, we show that ample divisors of low degree on an abelian variety have mild singularities in case the abelian variety is simple or the degree of the polarization is two.

We prove that separable extensions of noetherian rings and finite \'etale morphisms of noetherian schemes give rise to separable extensions of singularity categories.

This paper gives conditions for a singular foliation to be resolved.

The article has been withdrawn by the author due to the existence of counterexamples.

We present scheme theoretic methods that apply to the study of secant varieties. This mainly concerns finite schemes and their smoothability. The theory generalises to the base fields of any characteristic, and even to non-algebraically…

In this note we make a minor correction to the paper ``Simplicial monoids and Segal categories."

The main goal of this paper is to study some local and global properties of secant varieties of algebraic curves. These results complement our previous work [8] by addressing issues given therein and providing solutions to problems raised…

We prove a specialization inequality relating the dimension of the complete linear series on a variety to the tropical complex of a regular semistable degeneration. Our result extends Baker's specialization inequality to arbitrary…

We discuss some "folklore" results on categorical crepant resolutions for varieties with quotient singularities.

We shall present an elementary approach to extremal decompositions of (quantum) covariance matrices determined by densities. We give a new proof on former results and provide a sharp estimate of the ranks of the densities that appear in the…

A general theorem on fibers of singular sets is presented.

Consider a smooth projective curve and a given embedding into projective space via a sufficiently positive line bundle. We can form the secant variety of $k$-planes through the curve. These are singular varieties, with each secant variety…

We list combinatorial criteria of some singularities, which appear in the Minimal Model Program or in the study of (singular) Fano varieties, for spherical varieties. Most of the results of this paper are already known or are quite easy…

To a singular foliation on the plane corresponds a circular boundary at infinity endowed with a pre-lamination on the circle. We solve the converse direction. We determine which pre-lamination on the circle are boundary at infinity of a…