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

We derive simple forms for saddle-node singular points of analytic foliations in the real or complex plane just by gluing foliated complex manifolds. We give the versal analytic deformation of the simplest model. We also derive a unique…

We study linearly independent complex line fields on almost-complex manifolds, which is a topic of long-standing interest in differential topology and complex geometry. A necessary condition for the existence of such fields is the vanishing…

We generalise a construction of Landsberg, which associates certain Clifford algebra representations to Severi varieties. We thus obtain a new proof of Russo's Divisibility Property for LQEL varieties.

This note continues our previous work on special secant defective (specifically, conic connected and local quadratic entry locus) and dual defective manifolds. These are now well understood, except for the prime Fano ones. Here we add a few…

We obtain sharp lower and upper bounds for the number of maximal (under inclusion) independent sets in trees with fixed number of vertices and diameter. All extremal trees are described up to isomorphism.

We study the behavior of irregular fibrations of a variety under derived equivalence of its bounded derived category. In particular we prove the derived invariance of the existence of an irregular fibration over a variety of general type,…

We describe a deterministic process to associate a practical, permanent label to isomorphism classes of abelian varieties defined over finite fields with commutative endomorphism algebra as long as they are ordinary or defined over a prime…

We study finite morphisms of varieties and the link between their top multiplicity loci under certain assumptions. More precisely, we focus on how to determine that link in terms of the spaces of arcs of the varieties.

We complete the classification of wonderful varieties initiated by D. Luna. We review the results that reduce the problem to the family of primitive varieties, and report the references where some of them have already been studied. Finally,…

Revised version. Proper credits added. In this paper we study divisorial extremal neighborhoods f:Y-->X, such that X is a cAn type three dimensional terminal singularity, and C=f(E) is a smooth curve, where E is the f-exceptional divisor.…

In this paper we study analogues of the perfect splines for weighted Sobolev classes of functions defined on the half-line. Maximally oscillating splines play important role in the solution of certain extremal problems. In particular, using…

In this paper we study precise large deviations for the partial sums of a stationary sequence with a subexponential marginal distribution. Our main focus is on distributions which either have a regularly varying or a lognormal-type tail. We…

In this article, we give a complete description of the characteristic polynomials of supersingular abelian varieties over finite fields. We list them for the dimensions upto 7.

We prove that any finitely generated one ended group has linear end depth. Moreover, we give alternative proofs to theorems relating the growth of a finitely generated group to the number of its ends.

In this article we study certain specialization properties of the index of varieties defined by Koll\'{a}r.

We completely determine all semigroup [epigroup] varieties that are cancellable elements of the lattice of all semigroup [respectively epigroup] varieties.

In the present paper, we deform isolated singularities of a certain class of polar weighted homogeneous mixed polynomials, and show that there exists a deformation which has only definite fold singularities and mixed Morse singularities.

We prove that the Picard group of a regular simply connected variety over an algebraically closed field of arbitrary characteristic is finitely generated. The main difficulty to overcome is the unavailability of resolution of singularities.…

In this article we demonstrate the relationship between finitely exchangeable arrays and finitely exchangeable sequences. We then derive sharp bounds on the total variation distance between distributions of finitely and infinitely…

We show that the derived category of any singularity over a field of characteristic 0 can be embedded fully and faithfully into a smooth triangulated category which has a semiorthogonal decomposition with components equivalent to derived…