标题： 二重点除子的正性 显示英文标题

标题： Positivity of double point divisors

摘要： 一般投射到超曲面的非同构中心在某个有效除子的线性系统中移动，我们称这个除子为双点除子。 大卫·芒福德证明了外投影的双点除子总是无基点的，而博·伊利奇证明了它除了罗特簇之外总是丰沛的。 本文的第一个目的是证明外投影的双点除子在罗特情形之外总是非常丰沛的。 这回答了博·伊利奇提出的一个问题。 与外投影的情形不同，内投影的双点除子可能既不是无基点的也不是丰沛的。 然而，阿特苏希·诺马证明了它在一种情况下是半丰沛的，即一个簇既不是罗特簇，也不是曲线上的滚动簇，也不是第二个维内塞表面。 在本文中，我们将研究内投影的双点除子何时是无基点的或者大的。 显示英文摘要

摘要： The non-isomorphic locus of a general projection from an embedded smooth projective variety to a hypersurface moves in a linear system of an effective divisor which we call the double point divisor. David Mumford proved that the double point divisor from outer projection is always base point free, and Bo Ilic proved that it is ample except for a Roth variety. The first aim of this paper is to show that the double point divisor from outer projection is very ample except in the Roth case. This answers a question of Bo Ilic. Unlike the case of outer projection, the double point divisor from inner projection may not be base point free nor ample. However, Atsushi Noma proved that it is semiample except when a variety is neither a Roth variety, a scroll over a curve, nor the second Veronese surface. In this paper, we investigate when the double point divisor from inner projection is base point free or big.