MODULI OF WEIGHTED POINTED STABLE CURVES AND LOG CANONICAL MODELS OF Mg,n
نویسنده
چکیده
We establish nefness of certain tautological divisor classes onM0,n, and more generally on Hassett’s spacesMg,A, and prove thatMg,A is a log canonical model ofMg,n for every genus g and every weight vector A.
منابع مشابه
PROJECTIVITY OF THE MODULI SPACE OF α-STABLE CURVES AND THE LOG MINIMAL PROGRAM FOR Mg,n
For the moduli stacks of α-stable curves defined in [AFSv14], we prove nefness of natural log canonical divisors generalizing a well-known result of Cornalba and Harris for Mg,n. We deduce the projectivity of the good moduli spaces of α-stable curves and identify these moduli spaces with the log canonical models of Mg,n.
متن کاملOn Log Canonical Models of the Moduli Space of Stable Pointed Curves
n≥0 Γ(nKMg). Mg has been proven to be of general type for g ≥ 22 [EH,Fa,HaMu]. In particular in this case the finite generation of the canonical ring implies that the canonical model is birational to Mg. Recent progress has been made in this area. For example [BCHM] have proved the existence of canonical models in the case of smooth projective varieties of general type. A somewhat easier proble...
متن کاملSecond Flip in the Hassett-keel Program: Projectivity
For the moduli stacks of α-stable curves introduced in [AFSv15], we prove nefness of natural log canonical divisors generalizing a well-known result of Cornalba and Harris for the moduli stack of Deligne-Mumford stable curves. We then deduce the projectivity of the good moduli spaces of α-stable curves and identify these moduli spaces with the log canonical models of Mg,n appearing in the Hasse...
متن کاملLog Canonical Singularities and Complete Moduli of Stable Pairs
0.1. This paper consists of two parts. In the first part, assuming the log Minimal Model Program (which is currently only known to be true in dim ≤ 3), we construct the complete moduli of “stable pairs” (X,B) of projective schemes with divisors that generalize the moduli space of n-pointed stable curves Mg,n to arbitrary dimension. The construction itself is a direct generalization of that of [...
متن کاملChow Quotients of Grassmannians Ii
1.0 Properties of M0,n ⊂ M0,n. (1) M0,n has a natural moduli interpretation, namely it is the moduli space of stable n-pointed rational curves. (2) Given power series f1(z), . . . , fn(z) which we think of as a one parameter family in M0,n one can ask: What is the limiting stable n-pointed rational curve in M0,n as z → 0 ? There is a beautiful answer, due to Kapranov [Kapranov93a], in terms of ...
متن کامل