This article presents an algebraic proof of the invariance of plurigenera for families of smooth projective varieties under deformations.While Siu’s original proof relied on analytic tools such as multiplier ideal sh...This article presents an algebraic proof of the invariance of plurigenera for families of smooth projective varieties under deformations.While Siu’s original proof relied on analytic tools such as multiplier ideal sheaves and L2-extension theorems,our approach reformulates these techniques within the framework of algebraic geometry,emphasizing multiplier ideals,Castelnuovo-Mumford regularity,and Nadel vanishing theorem.Key steps include establishing the surjectivity of restriction maps for pluricanonical sections via careful analysis of base ideals and asymptotic multiplier ideals.This work aligns with recent efforts to translate Siu’s results into algebraic settings and provides a foundation for extending the invariance theorem to singular varieties.展开更多
In this paper, we determine the classification up to isomorphism and the central extensions of a class of Lie algebras B（q） of Block type, where q is a non-zero complex number.Our results generalize some previous re...In this paper, we determine the classification up to isomorphism and the central extensions of a class of Lie algebras B（q） of Block type, where q is a non-zero complex number.Our results generalize some previous results.展开更多
This paper deals with homology groups induced by the exterior algebra generated by the simplicial compliment of a simplicial complex K. By using ech homology and Alexander duality, the authors prove that there is a du...This paper deals with homology groups induced by the exterior algebra generated by the simplicial compliment of a simplicial complex K. By using ech homology and Alexander duality, the authors prove that there is a duality between these homology groups and the simplicial homology groups of K.展开更多
For a quantized enveloping algebra of finite type, one can associate a natural monomial to a dominant weight. We show that these monomials for types A5 and D4 are semitight(i.e., a Z-linear combination of elements in ...For a quantized enveloping algebra of finite type, one can associate a natural monomial to a dominant weight. We show that these monomials for types A5 and D4 are semitight(i.e., a Z-linear combination of elements in the canonical basis) by a direct calculation.展开更多
文摘This article presents an algebraic proof of the invariance of plurigenera for families of smooth projective varieties under deformations.While Siu’s original proof relied on analytic tools such as multiplier ideal sheaves and L2-extension theorems,our approach reformulates these techniques within the framework of algebraic geometry,emphasizing multiplier ideals,Castelnuovo-Mumford regularity,and Nadel vanishing theorem.Key steps include establishing the surjectivity of restriction maps for pluricanonical sections via careful analysis of base ideals and asymptotic multiplier ideals.This work aligns with recent efforts to translate Siu’s results into algebraic settings and provides a foundation for extending the invariance theorem to singular varieties.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11201253,11401570)the Natural Science Foundation of Jiangsu Province(Grant No.BK20140177)the Scientific Research Projects(Youth Project)of Xuzhou Institute of Technology(Grant No.XKY2013315)
文摘In this paper, we determine the classification up to isomorphism and the central extensions of a class of Lie algebras B（q） of Block type, where q is a non-zero complex number.Our results generalize some previous results.
基金supported by the National Natural Science Foundation of China(Nos.11371093,11261062,11471167)
文摘This paper deals with homology groups induced by the exterior algebra generated by the simplicial compliment of a simplicial complex K. By using ech homology and Alexander duality, the authors prove that there is a duality between these homology groups and the simplicial homology groups of K.
文摘For a quantized enveloping algebra of finite type, one can associate a natural monomial to a dominant weight. We show that these monomials for types A5 and D4 are semitight(i.e., a Z-linear combination of elements in the canonical basis) by a direct calculation.
