Related papers: On semipositivity, injectivity and vanishing theor…
This text is a draft of the review paper on projectively dual varieties. Topics include dual varieties, Pyasetskii pairing, discriminant complexes, resultants and schemes of zeros, secant and tangential varieties, Ein theorems, applications…
In recent years several classes of structured matrices are extended to classes of tensors in the context of tensor complementarity problem. The tensor complementarity problem is a class of nonlinear complementarity problem where the…
In this note, we state various generalisations of the Nakano vanishing theorem under weak positivity assumptions, and compare them with the known results.
We describe rings over which every right module is almost injective. We give a description of rings over which every simple module is a almost projective.
We show that the term equivalence between MV-algebras and MV-semirings lifts to involutive residuated lattices and a class of semirings called \textit{involutive semirings}. The semiring perspective helps us find a necessary and sufficient…
We propose a new class of filtered vector bundles, which is related to variation of (mixed) Hodge structures and give a slight generalization of the Fujita--Zucker--Kawamata semipositivity theorem.
We give an analytic version of the injectivity theorem by using multiplier ideal sheaves, and prove some extension theorems for the adjoint bundle of dlt pairs. Moreover, by combining techniques of the minimal model program, we obtain some…
We prove an injectivity theorem for the cohomology of the Du Bois complexes of varieties with isolated singularities. We use this to deduce vanishing statements for the cohomologies of higher Du Bois complexes of such varieties. Besides…
In this survey article we outline the history of the twin theories of weak normality and seminormality for commutative rings and algebraic varieties with an emphasis on the recent developments in these theories over the past fifteen years.…
This survey aims to give an overview of several substantial developments of the last 50 years in the structure theory of regular semigroups and to shed light on their impact on other parts of semigroup theory.
We discuss vanishing theorems for projective morphisms between complex analytics spaces and some related results. They will play a crucial role in the minimal model theory for projective morphisms of complex analytic spaces. Roughly…
We revisit the notion of flatness for semimodules over semirings. In particular, we introduce and study a new notion of uniformly flat semimodules based on the exactness of the tensor functor. We also investigate the relations between this…
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.
This is a non-technical survey of a recent theory of valuations on manifolds constructed in math.MG/0503397, math.MG/0503399, math.MG/0509512, math.MG/0511171 and actually a guide to this series of articles. We review also some recent…
This is a mostly expository paper, intended to explain a very natural relationship between two a priori distinct notions appearing in the literature: Generic Vanishing in the context of vanishing theorems and birational geometry, and…
A working mathematician's summary of many results on the derived category, perverse sheaves, and vanishing cycles. This is the August 2025 version, with a completely revised section on vanishing cycles.
We state the fundamental theorem of projective geometry for semimodules over semirings, which is facilitated by recent work in the study of bases in semimodules defined over semirings. In the process we explore in detail the linear algebra…
In this short note we present several infinite dimensional theorems which generalize corresponding facts from the finite dimensional differential inclusions theory.
Finite mixture models have been a very important tool for exploring complex data structures in many scientific areas, for example, economics, epidemiology, finance. In the past decade, semiparametric techniques have been popularly…
The purpose of this paper is to give two supplements for vanishing theorems: One is a relative version of the Kawamata-Viehweg-Nadel type vanishing theorem, which is obtained from an observation for the variation of the numerical dimension…