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Shafarevich Seminar
June 5, 2012 15:00, Moscow, Steklov Mathematical Institute, room 540 (Gubkina 8)
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How to calculate A-Hilb $CC^n$ for $1/r(a,b,1,\dots,1)$
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
$A=1/r(a,b,1,\dots,1)$ (with 1 repeated $n-2$ times) has a crepant resolution if and only if the
point nearest the ($x_1=0$) face is $P_c=1/r(1,d,c,\dots,c)$ where $d=r-(n-2)c-1>0$, and every entry of the Hirzebruch-Jung continued fraction of $r/d$ is congruent to $2\;\operatorname{mod} n-2$. In these cases a
modification of the Nakamura-Craw-Reid algorithm calculates the A-Hilbert 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
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