Forgetful Maps between Deligne-mostow Ball Quotients

نویسنده

  • MARTIN DERAUX
چکیده

We study forgetful maps between Deligne-Mostow moduli spaces of weighted points on P, and classify the forgetful maps that extend to a map of orbifolds between the stable completions. The cases where this happens include the Livné fibrations and the Mostow/Toledo maps between complex hyperbolic surfaces. They also include a retraction of a 3-dimensional ball quotient onto one of its 1-dimensional totally geodesic complex submanifolds.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Hurwitz Spaces and Moduli Spaces as Ball Quotients via Pull-back

We define hypergeometric functions using intersection homology valued in a local system. Topology is emphasized; analysis enters only once, via the Hodge decomposition. By a pull-back procedure we construct special subsets Sπ , derived from Hurwitz spaces, of Deligne-Mostow moduli spaces DM(n, μ). Certain DM(n, μ) are known to be ball quotients, uniformized by hypergeometric functions valued in...

متن کامل

Hurwitz ball quotients

We consider the analogue of Hurwitz curves, smooth projective curves C of genus g ≥ 2 that realize equality in the Hurwitz bound |Aut(C)| ≤ 84(g − 1), to smooth compact quotients S of the unit ball in C. When S is arithmetic, we show that |Aut(S)| ≤ 288e(S), where e(S) is the (topological) Euler characteristic, and in the case of equality show that S is a regular cover of a particular Deligne–M...

متن کامل

Linear Manifolds in the Moduli Space of One-forms

We study closures of GL+2 (R)-orbits on the total space ΩMg of the Hodge bundle over the moduli space of curves under the assumption that they are algebraic manifolds. We show that, in the generic stratum, such manifolds are the whole stratum, the hyperelliptic locus or parameterize curves whose Jacobian has additional endomorphisms. This follows from a cohomological description of the tangent ...

متن کامل

Moduli Space of Cubic Surfaces as Ball Quotient via Hypergeometric Functions

We describe hypergeometric functions of Deligne-Mostow type for open subsets of the configuration space of six points on P, induced from those for seven points on P. The seven point ball quotient example DM(2, 1) does not appear on Mostow’s original list [9], but does appear on Thurston’s corrected version [12]. We show that DM(2, 1) is a finite cover of the moduli space of cubic surfaces MC en...

متن کامل

The Tropicalization of the Moduli Space of Curves

We show that the skeleton of the Deligne-MumfordKnudsen moduli stack of stable curves is naturally identified with the moduli space of extended tropical curves, and that this is compatible with the “naive” set-theoretic tropicalization map. The proof passes through general structure results on the skeleton of a toroidal Deligne-Mumford stack. Furthermore, we construct tautological forgetful, cl...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008