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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 A-Hilb $CC^n$ 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 $n-2$ times) has a crepant resolution if and only if the point nearest the ($x_1=0$) face is $P_c=1/r(1,d,c,…,c)$ 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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