Related papers: Relative Bertini type theorem for multiplier ideal…

Semistable reduction theorem for projective morphisms in the category of complex analytic spaces is established.

We are proving a Bernstein type inequality in the shift-invariant spaces of $L_2(R)$.

We shall prove an extension of the semipositivity theorem for the case of reducible algebraic fiber spaces.

Given a boundary divisor $B$ on a projective toric variety $X$ such that $(X, B)$ is klt, we establish the Kawamata-Viehweg vanishing theorem for $(X, B)$.

For a smooth proper scheme over a local field of mixed characteristics which has semistable reduction we define the category of its semistable etale sheaves and under certain hypothesis we prove the appropriate semistable comparison…

In this paper, we establish a logarithmic vanishing theorem on weakly pseudoconvex K\"ahler manifolds, where the divisor may have infinitely many irreducible components. This result serves as a generalization of Norimatsu's findings on…

Let $X$ be an irreducible projective variety and $f$ a morphism $X \rightarrow \mathbb{P}^n$. We give a new proof of the fact that the preimage of any linear variety of dimension $k\ge n+1-\dim f(X)$ is connected. We prove that the…

The present note generalizes Debarre's Bertini-type results for in- verse images of Schubert varieties with the extension of formal func- tions.

We prove an elegant structure theorem for log de Rham-Witt sheaves with vanishing along an effective Cartier divisor $D$ defined in arXiv:2403.18763, answering a question of Shuji Saito during the Mainz conference and a question of Yigeng…

The paper offers versions of Hilbert's Irreducibility Theorem for the lifting of points in a cyclic subgroup of an algebraic group to a ramified cover. A version of Bertini Theorem in this context is also obtained.

We present a relative form of the Toponogov comparison theorem.

We prove a relative Kawamata Viehweg vanishing type theorem for birational morphisms. We use this to prove a Grauert Riemenschneider theorem over log canonical threefolds without zero dimensional log canonical centers, in residue…

Let $X$ be a scheme, proper over a commutative noetherian ring $A$. We introduce the concept of an ample filter of invertible sheaves on $X$ and generalize the most important equivalent criteria for ampleness of an invertible sheaf. We also…

New splitting theorems in a semi-Riemannian manifold which admits an irrotational vector field (not necessarily a gradient) with some suitable properties are obtained. According to the extras hypothesis assumed on the vector field, we can…

On smooth projective variety, for a reduced effective divisor which is weakly ample in the sense of cohomology, we introduce a Kadaira--Saito vanishing theorem for it.

We prove a Generic Vanishing Theorem for coherent sheaves on an abelian variety over an algebraically closed field $k$. When $k=\CC$ this implies a conjecture of Green and Lazarsfeld.

We show that any pseudo-effective divisor on a normal surface decomposes uniquely into its "integral positive" part and "integral negative" part, which is an integral analog of Zariski decompositions. By using this decomposition, we give…

We establish a version of the Beurling-Pollard theorem for operator synthesis and apply it to derive some results on linear operator equations and to prove a Beurling-Pollard type theorem for Varopoulos tensor algebras. Additionally we…

In this paper, we prove a version of the arithmetic Bertini theorem asserting that there exists a strictly small and generically smooth section of a given arithmetically free graded arithmetic linear series.

After reviewing Bertini's life story, a fascinating drama, we make a critical examination of the old statements and proofs of Bertini's two fundamental theorems, the theorem on variable singular points and the theorem on reducible linear…