相关论文: Relative Chow-Kunneth decompositions for conic bun…

In an earlier paper we conjectured a relation between the quantum $\mathcal D$-modules of a smooth variety $X$ and the projectivisation of a direct sum of line bundles over it. In this paper we prove the conjecture when $X$ is a complete…

The Beilinson-Bloch type conjectures predict that the low degree rational Chow groups of intersections of quadrics are one dimensional. This conjecture was proved by Otwinowska. Making use of homological projective duality and the recent…

A $\mathbb Q$-conic bundle is a proper morphism from a threefold with only terminal singularities to a normal surface such that fibers are connected and the anti-canonical divisor is relatively ample. We study the structure of $\mathbb…

We introduce certain quiver analogue of the determinantal variety. We study the Kempf-Lascoux-Weyman's complex associated to a line bundle on the variety. In the case of generalized Kronecker quivers, we give a sufficient condition on when…

We give a simplified proof (in characteristic zero) of the decomposition theorem for complex projective varieties with klt singularities and numerically trivial canonical bundle. The proof rests in an essential way on most of the partial…

We study real double covers of $\mathbb P^1\times\mathbb P^2$ branched over a $(2,2)$-divisor, which have the structure of a conic bundle threefold with smooth quartic discriminant curve via the second projection. In each isotopy class of…

Using a codimension-$1$ algebraic cycle obtained from the Poincar\'e line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian variety $A$ and showed that the Fourier transform induces a decomposition of the Chow…

A smooth intersection $Y$ of two quadrics in $\mathbb{P}^{2g+1}$ has Hodge level 1. We show that such varieties $Y$ have a multiplicative Chow-K\"unneth decomposition, in the sense of Shen-Vial. As a consequence, a certain tautological…

Given a connection on a meromorphic vector bundle over a compact Riemann surface with reductive Galois group, we associate to it a projective variety. Connections such that their associated projective variety are curves can be classified,…

We describe the integral equivariant cohomology ring of a weighted projective space in terms of piecewise polynomials, and thence by generators and relations. We deduce that the ring is a perfect invariant, and prove a Chern class formula…

Let T be a general bidegree (2,2) divisor in the product of two projective planes. Recently A.Verra proved that the existence of two conic bundle structures (c.b.s.) on T implies a new counterexample to the Torelli theorem for Prym…

Noncommutative (NC) sphere is introduced as a quotient of the enveloping algebra of the Lie algebra su(2). Using the Cayley-Hamilton identities we introduce projective modules which are analogues of line bundles on the usual sphere (we call…

A double cover $Y$ of $\mathbb{P}^1 \times \mathbb{P}^2$ ramified over a general $(2,2)$-divisor will have the structure of a geometrically standard conic bundle ramified over a smooth plane quartic $\Delta \subset \mathbb{P}^2$ via the…

We construct a three-parameter family of non-hyperelliptic and bielliptic plane genus-three curves whose associated Prym variety is two-isogenous to the Jacobian variety of a general hyperelliptic genus-two curve. Our construction is based…

In this paper we count the number of isomorphism classes of geometrically indecomposable quasi-parabolic structures of a given type on a given vector bundle on the projective line over a finite field. We give a conjectural cohomological…

We show that for a K3 surface X the finitely generated subring R(X) of the Chow ring introduced by Beauville and Voisin is preserved under derived equivalences. This is proved by analyzing Chern characters of spherical bundles. As for a K3…

Let $C$ be a genus 2 curve and $\su$ the moduli space of semi-stable rank 2 vector bundles on $C$ with trivial determinant. In \cite{bol:wed} we described the parameter space of non stable extension classes (invariant with respect to the…

Given a family of based CW-pairs $(\underline{X},\underline{A})=\{(X;A)\}^m_{i=1}$ together with an abstract simplicial complex $K$ with $m$ vertices, there is an associated based CW-complex $Z(K;(\underline{X},\underline{A}))$ known as a…

We classify equivariant topological complex vector bundles over real projective plane under a compact Lie group (not necessarily effective) action. It is shown that nonequivariant Chern classes and isotropy representations at (at most)…

Given a discrete subgroup $\Gamma$ of finite co-volume of $\mathrm{PGL}(2,\mathbb{R})$, we define and study parabolic vector bundles on the quotient $\Sigma$ of the (extended) hyperbolic plane by $\Gamma$. If $\Gamma$ contains an…