相关论文: Special effect varieties in higher dimension

In this paper, we study dimensions of some varieties, that were introduced recently by Kisin in order to prove modularity of some Galois representations. In fact, we mainly consider a special case for which we obtain an estimation of the…

We give divisibility results for the (global) characteristic varieties of hypersurface complements expressed in terms of the local characteristic varieties at points along one of the irreducible components of the hypersurface. As an…

I propose a few increasingly stronger "superadditivity" conjectures regarding the behavior of Kodaira dimension under morphisms of smooth quasi-projective complex varieties.

The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.

We give a survey of the incredibly beautiful amount of geometry involved with the problem of realizing a projective variety as hyperplane section of another variety.

We consider linear systems on toric varieties of any dimension, with invariant base points, giving a characterization of special linear systems. We then make a new conjecture for linear systems on rational surfaces.

We analyze the massive 4D scalar multiplet in 'reformulated' projective N=2 superspace (hyperspace) from both 4D and 6D perspectives.

We review some aspects of theories with compact extra dimensions. We consider the motivation and the theoretical basis of Large, Universal and Warped Extra Dimensions. We focus on those aspects that are potentially relevant in the…

We generalize the definition of alpha invariant to arbitrary codimension. We also give a lower bound of these alpha invariants for K-semistable Q-Fano varieties and show that we can characterize projective spaces among all K-semistable Fano…

We study arrangements of $m$ hyperplanes in the $n$-dimensional real projective space, with a special focus on $m=n+3$ and $n=3$ or $n=4$.

We determine set theoretic defining equations for the third secant variety of the Segre product of $n$ projective spaces, and from the proof of the main statement we derive an upper bound for the degrees of these equations.

We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.

We study $(2,2)$ and $(4,4)$ supersymmetric theories with superspace higher derivatives in two dimensions. A characteristic feature of these models is that they have several different vacua, some of which break supersymmetry. Depending on…

We extend our classification of special Cremona transformations whose base locus has dimension at most three to the case when the target space is replaced by a (locally) factorial complete intersection.

A birational map from a projective space onto a not too much singular projective variety with a single irreducible non-singular base locus scheme (special birational transformation) is a rare enough phenomenon to allow meaningful and…

We introduce and study coordinate-wise powers of subvarieties of $\mathbb{P}^n$, i.e. varieties arising from raising all points in a given subvariety of $\mathbb{P}^n$ to the $r$-th power, coordinate by coordinate. This corresponds to…

We study the box dimensions of self-affine sets in $\mathbb{R}^3$ which are generated by a finite collection of generalised permutation matrices. We obtain bounds for the dimensions which hold with very minimal assumptions and give rise to…

We study subvarieties of a general projective degree $d$ hypersurface $X_d\subset \mathbf P^n$. Our main theorem, which improves previous results of L. Ein and C. Voisin, implies in particular the following sharp corollary: any subvariety…

In an unpublished preprint, A. King conjectured that there are tilting bundles over projective varieties which are obtained as invariant quotients of affine spaces for linear actions of reductive groups. The goal of this paper is to give…

In this paper we describe the notion of a toric supervariety, generalizing that of a toric variety from the classical setting. We give a combinatorial interpretation of the category of quasinormal toric supervarieties with one odd dimension…