论文标题
期望出乎意料：量化意外突出的持久性
Expecting the unexpected: quantifying the persistence of unexpected hypersurfaces
论文作者
论文摘要
如果$ x \ subset \ mathbb p^n $是一个减少的子处理，我们说，如果在一般点$ p $上强加了多重$ m $ $ m $ $ p $的$ t $ t $ $ t $ t $的意外超出表面，则无法对$ t $ x $ x $ x $ x $ x $ x $ x $ t $ t $ x $ x $ p $的预期条件施加预期数量。保证出现意外突出或确保无法发生的条件不能很好地理解。我们介绍了研究意外事性的新方法，例如使用通用初始理想和部分消除理想，以阐明何时以及何时无法发生。我们还表现出$ x $的代数和几何特性，在某些情况下保证，在其他情况下，$ x $具有某些意外性。此外，我们制定了一种量化意想不到的新方法（我们的AV序列），这使我们可以检测到意外事性随着$ t $的增加而持续的程度，但$ t-m $仍然恒定。最后，我们研究了$ x $的希尔伯特功能的意外程度。
If $X \subset \mathbb P^n$ is a reduced subscheme, we say that $X$ admits an unexpected hypersurface of degree $t$ for multiplicity $m$ if the imposition of having multiplicity $m$ at a general point $P$ fails to impose the expected number of conditions on the linear system of hypersurfaces of degree $t$ containing $X$. Conditions which either guarantee the occurrence of unexpected hypersurfaces, or which ensure that they cannot occur, are not well understand. We introduce new methods for studying unexpectedness, such as the use of generic initial ideals and partial elimination ideals to clarify when it can and when it cannot occur. We also exhibit algebraic and geometric properties of $X$ which in some cases guarantee and in other cases preclude $X$ having certain kinds of unexpectedness. In addition, we formulate a new way of quantifying unexpectedness (our AV sequence), which allows us detect the extent to which unexpectedness persists as $t$ increases but $t-m$ remains constant. Finally, we study to what extent we can detect unexpectedness from the Hilbert function of $X$.
