论文标题
具有属性$ {\ bf n} _ {3,3} $的表面的分类和几何属性
Classification and geometric properties of surfaces with property ${\bf N}_{3,3}$
论文作者
论文摘要
让$ x $成为投射空间中Codimension $ e $的封闭式子处理。一个人说$ x $满足属性$ {\ bf n} _ {d，p} $，如果均质坐标环的$ i $ th syzygies是由$ <d+i $的元素生成的，$ <d+i $ for $ 0 \ le i \ le i \ le i \ le p $。满足属性$ {\ bf n} _ {2，e} $的光滑投射品种的几何和代数属性是一个经典的结果。本文的目的是研究下一个情况：$ \ bbb p^5 $满足属性$ {\ bf n} _ {3,3} $的投射表面。特别是，我们使用邻接映射对此类品种进行分类，并且还通过使用Macaulay 2进行的计算来提供示例的示例。作为冠状动物，我们研究了CI-Biliaison等效类别的平滑投射表面，$ 10 $ 10 $ $ 10 $满意的财产$ {\ bf n} _ _ _ _ {3,3,3,3，cucic of os of os of of of Macaulay $ 10。
Let $X$ be a closed subscheme of codimension $e$ in a projective space. One says that $X$ satisfies property ${\bf N}_{d,p}$, if the $i$-th syzygies of the homogeneous coordinate ring are generated by elements of degree $<d+i$ for $0\le i\le p$. The geometric and algebraic properties of smooth projective varieties satisfying property ${\bf N}_{2,e}$ are well understood, and the complete classification of these varieties is a classical result. The aim of this paper is to study the next case: projective surfaces in $\Bbb P^5$ satisfying property ${\bf N}_{3,3}$. In particular, we give a classification of such varieties using adjunction mappings and we also provide illuminating examples of our results via calculations done with Macaulay 2. As corollaries, we study the CI-biliaison equivalence class of smooth projective surfaces of degree $10$ satisfying property ${\bf N}_{3,3}$ on a cubic fourfold.
