Giovedì 15 Giugno alle ore 14:15, Sara Angela Filippini (Università del Salento) terrà il seminario di Geometria dal titolo "Residual intersections and Schubert varieties".
Abstract: The notion of residual intersections was introduced by Artin and Nagata. Roughly speaking, given an algebraic variety $X$ and a closed subscheme $Y$ in $X$, which is contained in another closed subscheme $Z$, then a closed subscheme $W$ such that $W \cup Y = Z$ is a residual intersection of $Y$ in $Z$.
This idea can be formalized as follows: Let $I$ be an ideal in a local Cohen-Macaulay ring $R$, and $A = (a_1, \ldots, a_s) \subsetneq I$. Then $J = A:I$ is called an s-residual intersection of $I$ if $ht(J) \geq s \geq ht(I)$. Residual intersections provide a generalization of linkage. Indeed, if $J = A:I$ and $I = A:J$ for $A$ a regular sequence, $I$ and $J$ are said to be linked.
I will show how results of Huneke and of Kustin and Ulrich on residual intersections for standard deteminantal ideals and Pfaffian ideals respectively arise in the context of ideals of Schubert varieties in the big opposite cell of homogeneous spaces. This is joint work with J. Torres and J. Weyman.
Il seminario si svolgerà in presenza presso l'aula M1. Per ulteriori informazioni, e per il link Teams per seguire il seminario a distanza, si può contattare gli organizzatori all'email email@example.com.
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