Mathematics – Algebraic Geometry
Scientific paper
2006-02-27
Journal f\"ur die reine und angewandte Mathematik (Crelles Journal). Volume 2010, Issue 639, Pages 39-71
Mathematics
Algebraic Geometry
minor tweaks, addition of Chirivi-Littelmann example, and references to subsequent work of Lieblich and Starr
Scientific paper
The space of subvarieties of P^n with a fixed Hilbert polynomial is not complete. Grothendieck defined a completion by relaxing "variety" to "scheme", giving the complete_Hilbert scheme_ of subschemes of P^n with fixed Hilbert polynomial. We instead relax "sub" to "branch", where a_branchvariety of_ P^n is defined to be a_reduced_ (though possibly reducible) scheme_with a finite morphism to_ P^n. Our main theorems are that the moduli stack of branchvarieties of P^n with fixed Hilbert polynomial and total degrees of i-dimensional components is a proper (complete and separated) Artin stack with finite stabilizer, and has a coarse moduli space which is a proper algebraic space. Families of branchvarieties have many more locally constant invariants than families of subschemes; for example, the number of connected components is a new invariant. In characteristic 0, one can extend this count to associate a Z-labeled rooted forest to any branchvariety.
Alexeev Valery
Knutson Allen
No associations
LandOfFree
Complete moduli spaces of branchvarieties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Complete moduli spaces of branchvarieties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Complete moduli spaces of branchvarieties will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-485919