Related papers: On generalized canonical bundle formula and bounde…
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 introduce the notion of a Lie algebroid structure on an affine bundle whose base manifold is fibred over the real numbers. It is argued that this is the framework which one needs for coming to a time-dependent generalization of the…
We give a proof of generalizations of the classical Arakelov inequality valid for the degree $d$ of the relative canoincal bundle of a family of curves of genus $g$ over a complete curve of genus $p$ under the assumption that the monodromy…
In the present paper, we give an upper bound for the generic degree of the generalized Verschiebung between the moduli spaces of rank two stable bundles with trivial determinant.
We present here some conjectures on the diagonalizability of uniform principal bundles on rational homogeneous spaces, that are natural extensions of classical theorems on uniform vector bundles on the projective space, and study the…
We shall show how to decompose, by functorial and canonical fibrations, arbitrary $n$-dimensional complex projective {Although the geometric results apply to compact K\" ahler manifolds without change, we consider here for simplicity this…
We introduce the notion of basic slc-trivial fibrations. It is a generalization of that of Ambro's lc-trivial fibrations. Then we study fundamental properties of basic slc-trivial fibrations by using the theory of variations of mixed Hodge…
We classify all the surfaces of general type whose canonical map is composed with a pencil if they are the quotient of the diagonal action by an Abelian group acting over the product of two curves. As far as we know all the previous…
First, we prove that the set of $n\times n$ complex matrices is the closure of a certain open subset whose elements have a very specific canonical form under congruence, which is uniquely determined up to the values of some parameters, but…
We construct a conic Lagrangian in the cotangent bundle of the moduli stack of $G$-bundles over the universal curve, restricting to the global nilpotent cone for each curve. It gives rise to a singular support condition suitable for the…
In this article we study modules over wild canonical algebras which correspond to extension bundles [9] over weighted projective lines. We prove that all modules attached to extension bundles can be established by matrices with coefficients…
The aim of this article is to make a first step towards the classification of complex normal affine $\mathbb G_a$-threefolds $X$. We consider the case where the restriction of the quotient morphism $\pi\colon X\to S$ to $\pi^{-1}(S_*)$,…
The moduli space of canonical divisors (with prescribed zeros and poles) on nonsingular curves is not compact since the curve may degenerate. We define a proper moduli space of twisted canonical divisors in the moduli space of…
We introduce the notion of locally trivial quantum principal bundles. The base space and total space are compact quantum spaces (unital $C^{\star}$-algebras), the structure group is a compact matrix quantum group. We prove that a quantum…
We prove birational boundedness results on complete intersections with trivial canonical class of base point free divisors in (some version of) Fano varieties. Our results imply in particular that Batyrev-Borisov toric construction produces…
We study the analytic and topological invariants associated with complex normal surface singularities. Our goal is to provide topological formulae for several discrete analytic invariants whenever the analytic structure is generic (with…
We define a categorical birational invariant for minimal geometrically rational surfaces with a conic bundle structure over a perfect field via components of a natural semiorthogonal decomposition. Together with the similar known result on…
In this paper, we studied the map defined by a non-very ample line bundle on some special irregular varieties. As to this topic, it is well known that for a line bundle $L$ on an Abelian variety $A$, the linear system $|2L|$ is base point…
In previous work, the first three authors conjectured that the ring of regular functions on a natural class of affine log Calabi-Yau varieties (those with maximal boundary) has a canonical vector space basis parameterized by the integral…
In this paper I present a new geometric approach to the factorization rule for generalised theta functions. Let $X$ be an irreducible projective nodal curve with one singularity and let $Y$ be its normalization. Recently I have constructed…