Related papers: Determinant morphism for singular varieties

In this paper, which is the sequel to arXiv:1410.3742, we study the Frobenius pushforward of the structure sheaf on the adjoint varieties in type ${\bf A}_3$ and ${\bf A}_4$. We show that this pushforward sheaf decomposes into a direct sum…

A criterion for a functor between derived categories of coherent sheaves to be full and faithful is given. A semiorthogonal decomposition for the derived category of coherent sheaves on the intersection of two even dimensional quadrics is…

Given a sheaf on a projective space P^n we define a sequence of canonical and easily computable Chow complexes on the Grassmannians of planes in P^n, generalizing the Beilinson monad on P^n. If the sheaf has dimension k, then the Chow form…

Based on the recent developments in the irregular Riemann-Hilbert correspondence for holonomic D-modules and the Fourier-Sato transforms for enhanced ind-sheaves, we study the Fourier transforms of some irregular holonomic D-modules. For…

We study the following generalization of singularity categories. Let X be a quasi-projective Gorenstein scheme with isolated singularities and A a non-commutative resolution of singularities of X in the sense of Van den Bergh. We introduce…

For a smooth projective variety $X$ with exceptional structure sheaf, and $\operatorname{Hilb}^2X$ the Hilbert scheme of two points on $X$, we show that the Fourier-Mukai functor $\mathbf{D}^{\mathrm{b}}(X)…

Let $\mhu$ be the moduli space of semi-stable pure sheaves of class $u$ on a smooth complex projective surface $X$. We specify $u=(0,L,\chi(u)=0),$ i.e. sheaves in $u$ are of dimension $1$. There is a natural morphism $\pi$ from the moduli…

Let $\phi$ be a generically surjective morphism between direct sums of line bundles on $\proj{n}$ and assume that the degeneracy locus, $X$, of $\phi$ has the expected codimension. We call $B_{\phi} = \ker \phi$ a (first) Buchsbaum-Rim…

This paper answers a question of Demailly whether a smooth family of nonsingular projective varieties admits the deformation invariance of plurigenera affirmatively, and proves this more generally for a flat family of varieties with only…

By introducing a new invariant called the set of slidings, we give a complete strict classification of the class of germs of non-dicritical holomorphic foliations in the plan whose Camacho-Sad indices are not rational. Moreover, we will…

Building on the concept of a smooth DG algebra we define the notion of a smooth derived category. We the propose the definition of a categorical resolution of singularities. Our main example is the derived category $D(X)$ of quasi-coherent…

In this paper we study the incidence complex of an arbitrary morphism of locally free sheaves relative to an arbitrary quasi compact morphism of schemes. We prove it is a local complete intersection in the case when the sheaf morphism is…

An $F$-zip over a scheme $S$ over a finite field is a certain object of semi-linear algebra consisting of a locally free module with a descending filtration and an ascending filtration and a $\Frob_q$-twisted isomorphism between the…

Let X be a singular affine normal variety with coordinate ring R and assume that there is an R-order admitting a stability structure such that the scheme of relevant semistable representations is smooth, then we construct a partial…

Let $f : X \rightarrow Y$ be a dominant generically smooth morphism between irreducible smooth projective curves over an algebraically closed field $k$ such that ${\rm Char}(k)> \text{degree}(f)$ if the characteristic of $k$ is nonzero. We…

Let $U$ be a graded unipotent group over the complex numbers, in the sense that it has an extension $\hat{U}$ by the multiplicative group such that the action of the multiplicative group by conjugation on the Lie algebra of $U$ has all its…

We show that for flat morphisms between varieties with rational singularities, the higher direct images of the structure sheaf are locally free. As a consequence, the identity component of the relative Picard scheme is a smooth algebraic…

In this paper, we prove that the Grothendieck-Riemann-Roch formula in Deligne cohomology computing the determinant of the cohomology of a holomorphic vector bundle on the fibers of a proper submersion between abstract complex manifolds is…

We show that any normal irreducible affine $n$-dimensional $SL_n$-variety $X$ is determined by its automorphism group in the category of normal irreducible affine varieties: if $Y$ is an irreducible affine normal algebraic variety such that…

Fix a scheme $X$ over a field of characteristic zero that is equipped with an action of a reductive algebraic group $G$. We give necessary and sufficient conditions for a $G$-equivariant coherent sheaf on $X$ or a bounded-above complex of…