Remarks on the existence of Cartier divisors
نویسنده
چکیده
We characterize those invertible sheaves on a noetherian scheme which are definable by Cartier divisors and correct an erroneous counterexample in the literature.
منابع مشابه
Intersection Theory Class 7
I’d like to make something more explicit than I have. An effective Cartier divisor on a scheme is a closed subscheme locally cut out by one function, and that function is not a zero-divisor. (Translation: the zero-set does not contain any associated points.) PicX = group of line bundles = Cartier divisors modulo linear equivalence = Cartier divisors modulo principal Cartier divisors. We get a m...
متن کاملIntersection Theory Class 9
I have one update from last time, and this is aimed more at the experts. Rob pointed out that there was no reason that we know that a Cartier divisor can be expressed as a difference (or quotient) of effective Cartier divisors. More precisely, a Cartier divisor can be described cohomologically as follows. Let X be a scheme. We have a sheaf O of invertible functions. There is another sheaf K tha...
متن کاملCanonical rational equivalence of intersections of divisors
We consider the operation of intersecting with a locally principal Cartier divisor (i.e., a Cartier divisor which is principal on some neighborhood of its support). We describe this operation explicitly on the level of cycles and rational equivalences and as a corollary obtain a formula for rational equivalence between intersections of two locally principal Cartier divisors. Such canonical rati...
متن کاملK-Theory and Intersection Theory
2.1 Dimension and codimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Dimension relative to a base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Cartier divisors . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
متن کاملHomogeneous Coordinates and Quotient Presentations for Toric Varieties
Generalizing cones over projective toric varieties, we present arbitrary toric varieties as quotients of quasiaffine toric varieties. Such quotient presentations correspond to groups of Weil divisors generating the topology. Groups comprising Cartier divisors define free quotients, whereas Q-Cartier divisors define geometric quotients. Each quotient presentation yields homogeneous coordinates. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008