

Seminar of the Department of Algebra and of the Department of Algebraic Geometry (Shafarevich Seminar)
June 5, 2012 15:00, Moscow, Steklov Mathematical Institute, room 540 (Gubkina 8)






How to calculate AHilb $CC^n$ for $1/r(a,b,1,…,1)$
Reid Miles^{} ^{} Warwick and Sogang Univ.

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Abstract:
An elementary result says (in the coprime case) that the $n$dimensional Gorenstein quotient
$A=1/r(a,b,1,…,1)$ (with 1 repeated $n2$ times) has a crepant resolution if and only if the
point nearest the ($x_1=0$) face is $P_c=1/r(1,d,c,…,c)$ where $d=r(n2)c1>0$, and every entry of the HirzebruchJung continued fraction of $r/d$ is congruent to $2\;\operatorname{mod} n2$. In these cases a
modification of the NakamuraCrawReid algorithm calculates the AHilbert scheme, with some fun for large $n$. This talk is based on joint work with Sarah Davis and Timothy Logvinenko and overlaps in
part with Chapter 4 of Sarah Davis's 2011 Warwick PhD thesis.
Language: English

