Related papers: DB pairs and vanishing theorems

This paper reproves a general form of the Green-Lazarsfeld 'generic vanishing' theorem and more recent strengthenings, as well as giving some new applications.

There exists a well established differential topological theory of singularities of ordinary differential equations. It has mainly studied scalar equations of low order. We propose an extension of the key concepts to arbitrary systems of…

We give a new proof of the main theorem in the theory of C(6) small cancellation complexes. We prove the fundamental theorem of cubical small cancellation theory for C(9) cubical small cancellation complexes.

We prove the following theorem characterizing Du Bois singularities. Suppose that $Y$ is smooth and that $X$ is a reduced closed subscheme. Let $\pi : \tld Y \to Y$ be a log resolution of $X$ in $Y$ that is an isomorphism outside of $X$. If…

In this short note, we classify pairs of conjugacy classes of the symmetric group such that any non-linear irreducible character of the symmetric group vanishes on at least one of them.

We use the liftability of the relative Frobenius morphism of toric varieties and the strong liftability of toric varieties to prove the Bott vanishing theorem, the degeneration of the Hodge to de Rham spectral sequence and the…

An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with…

We show how classical and quantum dualities, as well as duality relations that appear only in a sector of certain theories ("emergent dualities"), can be unveiled, and systematically established. Our method relies on the use of morphisms of…

We prove the existence of $n$-complements for pairs with DCC coefficients and the ACC for minimal log discrepancies of exceptional singularities. In order to prove these results, we develop the theory of complements for real coefficients.…

Let $X$ be a variety and $H$ a Cartier divisor on $X$. We prove that if $H$ has Du Bois (or DB) singularities, then $X$ has Du Bois singularities near $H$. As a consequence, if $X \to S$ is a family over a smooth curve $S$ whose special…

We prove that every quasi-projective semi log canonical pair has a quasi-log structure with several good properties. It implies that various vanishing theorems, torsion-free theorem, and the cone and contraction theorem hold for semi log…

The suggestion that particles of the same kind may be indistinguishable in a fundamental sense, even so that challenges to traditional notions of individuality and identity may arise, has first come up in the context of classical…

We prove the Kawamata-Viehweg vanishing theorem for a large class of divisors on surfaces in positive characteristic. By using this vanishing theorem, Reider-type theorems and extension theorems of morphisms for normal surfaces are…

We define a class of singularity on arbitrary pairs of a normal variety and an effective $\mathbb{R}$-divisor on it, which we call pseudo-lc in this paper. This is a generalization of the usual lc singularity of pairs and log canonical…

The nonvanishing conjecture for projective log canonical pairs plays a key role in the minimal model program of higher dimensional algebraic geometry. The numerical nonvanishing conjecture considered in this paper is a weaker version of the…

In this paper we introduce a notion of rational singularities associated to pairs $(X, \ba^t)$ where $X$ is a variety, $\ba$ is an ideal sheaf and $t$ is a nonnegative real number. We prove that most standard results about rational…

We discuss a difference between the rational and the real non-vanishing conjecture for pseudo-effective log canonical divisors of log canonical pairs. We also show the log non-vanishing theorem for rationally connected varieties under…

We reprove and generalize the result that the intersection cohomology groups of a toric variety with coefficient in a nontrivial rank one local system vanish. We prove a similar vanishing result for a certain class of varieties on which a…

We generalize the notions of singularities and ordinary points from linear ordinary differential equations to D-finite systems. Ordinary points of a D-finite system are characterized in terms of its formal power series solutions. We also…

We prove that the non-vanishing conjecture holds for generalized lc pairs with a polarization.