ﻻ يوجد ملخص باللغة العربية
We study arc spaces and jet schemes of generic determinantal varieties. Using the natural group action, we decompose the arc spaces into orbits, and analyze their structure. This allows us to compute the number of irreducible components of jet schemes, log canonical thresholds, and topological zeta functions.
Let $Xsubset mathbb{P}^r$ be an integral and non-degenerate variety. Let $sigma _{a,b}(X)subseteq mathbb{P}^r$, $(a,b)in mathbb{N}^2$, be the join of $a$ copies of $X$ and $b$ copies of the tangential variety of $X$. Using the classical Alexander-Hir
In this paper we generalize the definitions of singularities of pairs and multiplier ideal sheaves to pairs on arbitrary normal varieties, without any assumption on the variety being Q-Gorenstein or the pair being log Q-Gorenstein. The main features
We generalise Flo{}ystads theorem on the existence of monads on the projective space to a larger set of projective varieties. We consider a variety $X$, a line bundle $L$ on $X$, and a base-point-free linear system of sections of $L$ giving a morphis
We study vector bundles on flag varieties over an algebraically closed field $k$. In the first part, we suppose $G=G_k(d,n)$ $(2le dleq n-d)$ to be the Grassmannian manifold parameterizing linear subspaces of dimension $d$ in $k^n$, where $k$ is an a
We develop an analogue of Eisenbud-Floystad-Schreyers Tate resolutions for toric varieties. Our construction, which is given by a noncommutative analogue of a Fourier-Mukai transform, works quite generally and provides a new perspective on the relati