Related papers: On divisorial (i) classes

Let $X$ be a smooth compact projective variety over $\mathbb C$. Let $H^2(\pi_1(X),\mathbb R)^{1,1}$ be the intersection of $H^{1,1}(X,{\mathbb R})$ with the image of the map $H^2(\pi_1(X),{\mathbb R})\to H^2(X)$ induced by the classifying…

In this paper we work with several divisors of a module $E \subseteq G \simeq R^{e}$ having rank $e$, such as the classical Fitting ideals of $E$ and of $G/E$, and the more recently introduced (generic) Bourbaki ideals $I(E)$ (A. Simis, B.…

This paper addresses Question 1 posed by Dipendra Prasad in his recent problem list: classify all irreducible smooth representations of an unramified reductive p-adic group such that the space of vectors fixed by the pro-unipotent radical…

We classify all Gieseker semi-stable sheaves on the complex projective plane that have dimension 1, multiplicity 6 and Euler characteristic 3. We show that their moduli space is birational to the blow-up at a special point of a certain…

We establish a new connection between the iHowe duality of type AIII established by Luo-Xu and the iSchur duality established by Bao-Wang. We show that iweight $\overline{\rho}$ space in the iHowe duality is naturally isomorphic to the…

In the moduli space $\mathcal{C}$ of complex cubic hypersurfaces $X\subset\mathbb{P}^5$, we study the condition that $X$ admits a net of polar quadrics whose discriminant locus is a $10$-nodal irreducible plane sextic curve. Our main result…

This note discusses the bijection between the exceptional subcategories of representations of quivers and generalized non-crossing partitions of Weyl groups. We give a new proof of the Ingalls-Thomas-Igusa-Schiffler bijection by using the…

Let R be the set of isomorphism classes of ideals in the Weyl algebra $A=A_{1}$, and let C be the set of isomorphism classes of triples (V; X, Y), where V is a finite-dimensional (complex) vector space, and X, Y are endomorphisms of V such…

We develop a reduction procedure which provides an equivalence (as highest weight categories) from an arbitrary block (defined in terms of the central character and the integral Weyl group) of the BGG category O for a general linear Lie…

In order to support the odd moduli in models of (type IIB) string compactification, we classify the Calabi-Yau threefolds with h^{1,1}<=4 which exhibit pairs of identical divisors, with different line-bundle charges, mapping to each other…

We show that Nichols algebras of most simple Yetter-Drinfeld modules over the projective special linear group over a finite field, corresponding to non-semisimple orbits, have infinite dimension. We spell out a new criterium to show that a…

For all the irreducible dual pairs of type I $(G,G')$, we analyze the restriction of the oscillator representation as a $(\mathfrak{g}', K')$-module, when $G'$ is the smaller group. For all $(G,G')$ in the stable range, as well as one more…

We establish the Noether inequality for projective $3$-folds. More precisely, we prove that the inequality $${\rm vol}(X)\geq \tfrac{4}{3}p_g(X)-{\tfrac{10}{3}}$$ holds for all projective $3$-folds $X$ of general type with either…

R. Rim\'anyi defined the incidence class of two singularities X and Y as $[X]|_Y$, the restriction of the Thom polynomial of X to Y. He conjectured that (under mild conditions) the incidence is not zero if and only if Y is in the closure of…

We make a very detailed analysis of the numerical properties of effective divisors whose support is contained in the exceptional locus of a birational morphism of smooth projective surfaces. As an application we extend Miyaoka's inequality…

In this paper, we first introduce geometric operations for linear categories, and as a consequence generalize Orlov's blow up formula [O04] to possibly singular local complete intersection centres. Second, we introduce refined blowing up of…

We give an easy diagrammatical description of the parabolic Kazhdan-Lusztig polynomials for the Weyl group $W_n$ of type $D_n$ with parabolic subgroup of type $A_n$ and consequently an explicit counting formula for the dimension of the…

Generalizing the results of 1211.6077 and 1703.00905, we prove a formula for the pushforward of an arbitrary analytic function of the exceptional divisor class of a weighted blowup of an algebraic variety centered at a smooth complete…

We prove an analogue of the Lefschetz (1,1) Theorem characterizing cohomology classes of Cartier divisors (or equivalently first Chern classes of line bundles) in the second integral cohomology. Let $X$ be a normal complex projective…

Following a general method proposed earlier, we construct here Wigner functions defined on coadjoint orbits of a class of semidirect product groups. The groups in question are such that their unitary duals consist purely of representations…