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首頁(yè)> 外文OA文獻(xiàn) >Triple canonical covers of varieties of minimal degree.\ud
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Triple canonical covers of varieties of minimal degree.\ud

機(jī)譯：最小程度的變體的三重規(guī)范封面。\ ud

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In this article we study pluriregular varieties X of general type with base-point-free canonical bundle whose canonical morphism has degree 3 and maps X onto a variety of minimal degree Y. We carry out our study from two different perspectives. First we study in Section 2 and Section 3 the canonical ring of X describing completely the degrees of its minimal generators. We apply this to the study of the projective normality of the images of the pluricanonical morphisms of X. Our study of the canonical ring of X also shows that, if the dimension of X is greater than or equal to 3, there does not exist a converse to a theorem of M. Green that bounds the degree of the generators of the canonical ring of X. This is in sharp contrast with the situation in dimension 2 where such converse exists, as proved by the authors in a previous work. Second, we study in Section 4, the structure of the canonical morphism of X. We use this to show among other things the nonexistence of some a priori plausible examples of triple canonical covers of varieties of minimal degree. We also characterize the targets of flat canonical covers of varieties of minimal degree. Some of the results of Section 4 are more general and apply to varieties X which are not necessarily regular, and to targets Y that are scrolls which are not of minimal degree.
機(jī)譯：在本文中，我們研究具有無(wú)基點(diǎn)規(guī)范束的一般類型的多元正則變種X，其規(guī)范態(tài)態(tài)為3級(jí)，并將X映射到各種最小度Y。我們從兩個(gè)不同的角度進(jìn)行研究。首先，我們?cè)诘?節(jié)和第3節(jié)中研究X的規(guī)范環(huán)，以完全描述其最小生成器的程度。我們將此用于研究X的多正規(guī)態(tài)的圖像的射影正態(tài)性。我們對(duì)X的正則環(huán)的研究還表明，如果X的維數(shù)大于或等于3，則不存在作者在先前的工作中證明，這與限制X的正則環(huán)的生成器的階的M. Green定理相反。這與存在逆的維2的情況形成鮮明對(duì)比。第二，我們?cè)诘?節(jié)中研究X的規(guī)范形態(tài)的結(jié)構(gòu)。除其他事項(xiàng)外，我們用它展示了某些最小程度的三重規(guī)范覆蓋的先驗(yàn)合理示例的不存在。我們還表征了最小程度的變體的標(biāo)準(zhǔn)規(guī)范封面的目標(biāo)。第4節(jié)中的某些結(jié)果較為籠統(tǒng)，適用于不一定是常規(guī)的品種X，也適用于不是最小程度的滾動(dòng)的目標(biāo)Y。

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