论文标题
Hitchin纤维化中的Orbifold奇点的镜子：case $（\ text {sl} _n，\ text {pgl} _n）$
Mirror of Orbifold Singularities in the Hitchin Fibration: the case $(\text{SL}_n,\text{PGL}_n)$
论文作者
论文摘要
我们研究了椭圆基因座上的单数$ \ text {sl} _n $ -Hitchin纤维的几何形状。我们表明，Orbifold的奇异性出现在$ \ text {pgl} _n $ -moduli space $ m^{ell}（\ text {pgl} _n）$时，当$ \ text {sl} _n $ sid $ m^$ m^{ell}（ell}（ell）我们的主要定理表明，在$ m^{ell}中支撑在Orbifold奇异性支撑的摩天大楼的傅立叶 - 木像变换（\ text {pgl} _n）$满足了弗伦克尔和维滕的构想。
We study the geometry of singular $\text{SL}_n$-Hitchin fibres over the elliptic locus. We show that orbifold singularities appear in the $\text{PGL}_n$-moduli space $M^{ell}(\text{PGL}_n)$ exactly when the $\text{SL}_n$ side $M^{ell}(\text{SL}_n)$ has a reducible Hitchin fibre. Our main theorem shows that the Fourier-Mukai transform of a skyscraper sheaf supported at an orbifold singularity in $M^{ell}(\text{PGL}_n)$ satisfies a version of the fractional Hecke eigenproperty, as conjectured by Frenkel and Witten.
