کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4665555 1633816 2015 44 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The monodromy groups of Dolgachev's CY moduli spaces are Zariski dense
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
The monodromy groups of Dolgachev's CY moduli spaces are Zariski dense
چکیده انگلیسی

Let Mn,2n+2Mn,2n+2 be the coarse moduli space of CY manifolds arising from a crepant resolution of double covers of PnPn branched along 2n+22n+2 hyperplanes in general position. We show that the monodromy group of a good family for Mn,2n+2Mn,2n+2 is Zariski dense in the corresponding symplectic or orthogonal group if n≥3n≥3. In particular, the period map does not give a uniformization of any partial compactification of the coarse moduli space as a Shimura variety whenever n≥3n≥3. This disproves a conjecture of Dolgachev. As a consequence, the fundamental group of the coarse moduli space of m   ordered points in PnPn is shown to be large once it is not a point. Similar Zariski-density result is obtained for moduli spaces of CY manifolds arising from cyclic covers of PnPn branched along m hyperplanes in general position. A classification towards the geometric realization problem of B. Gross for type A bounded symmetric domains is given.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 272, 26 February 2015, Pages 699–742
نویسندگان
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