SINGULARITIES WITH Gm-ACTION AND THE LOG MINIMAL MODEL PROGRAM FOR Mg
نویسندگان
چکیده
We give a precise formulation of the modularity principle for the log canonical models Mg(α) := Proj ⊕ d≥0 H (Mg , bd(KMg +αδ)c). We define a new invariant of Gorenstein curve singularities with Gm-action which can be used to predict the critical α-value at which a singularity first arises in the modular interpretation of Mg(α). We compute these critical α-values for large classes of singularities, including all ADE, toric planar, and unibranch Gorenstein singularities, and use these results to give a conjectural outline of the log MMP for Mg .
منابع مشابه
ar X iv : 0 90 2 . 06 48 v 2 [ m at h . A G ] 2 7 A pr 2 00 9 LOG CANONICAL SINGULARITIES ARE DU BOIS
A recurring difficulty in the Minimal Model Program (MMP) is that while log terminal sin-gularities are quite well behaved (for instance, they are rational), log canonical singularities are much more complicated; they need not even be Cohen-Macaulay. The aim of this paper is to prove that, as conjectured in [Kol92, 1.13], log canonical singularities are Du Bois. The concept of Du Bois singulari...
متن کاملModuli Spaces of Hyperelliptic Curves with a and D Singularities
We introduce moduli spaces of quasi-admissible hyperelliptic covers with at worst A and D singularities. Stability conditions for these moduli problems depend on two parameters describing allowable singularities. At the extreme values of the parameters, we obtain the stacks TAn and TDn of stable limits of An and Dn singularities, as well as the quotients of the miniversal deformation spaces of ...
متن کاملF-injective Singularities Are Du Bois
In this paper, we prove that singularities of F -injective type are Du Bois. This extends the correspondence between singularities associated to the minimal model program and singularities defined by the action of Frobenius in positive characteristic.
متن کاملEffect of commercial (vimang) and hydroalcoholic extract of Mangifera indica (Mango) on gentamicin-induced nephrotoxicity in rat
Objectives: Mangifera indica (Mango) is used in folk medicine for treatment of different types of diseases, and its anti-inflammatory and free radical scavenging activities have been demonstrated. The present study evaluated the effects of commercial (vimang) and hydroalcoholic extract of Mango on gentamicin-induced nephrotoxicity in rat. Materials and Methods: Female Wistar rats were treated ...
متن کاملInduction of Apoptosis on K562 Cell Line and Double Strand Breaks on Colon Cancer Cell Line Expressing High Affinity Receptor for Granulocyte Macrophage-Colony Stimulating factor (GM-CSF)
Background: Immunotoxins are comprised of both the cell targeting and the cell killing moieties. We previously established a new immunotoxin, i.e. Shiga toxin granulocyte macrophage-colony stimulating factor (StxA1-GM-CSF), comprises of catalytic domain of Stx, as a killing moiety and GM-CSF, as a cell targeting moiety. In this study, the ability of the immunotoxin to induce apoptosis and dou...
متن کامل