Intersection Theory Class 7
نویسنده
چکیده
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 map from Cartier divisors to Weil divisors that descends to PicX → AdimX−1X.
منابع مشابه
intersection theory and operators in Hilbert space
For an operator of a certain class in Hilbert space, we introduce axioms of an abstract intersection theory, which we prove to be equivalent to the Riemann Hypothesis concerning the spectrum of that operator. In particular if the nontrivial zeros of the Riemann zeta-function arise from an operator of this class, the original Riemann Hypothesis is equivalent to the existence of an abstract inter...
متن کاملThe edge intersection graphs of paths in a tree
The class of edge intersection graphs of a collection of paths in a tree (EPT graphs) is investigated, where two paths edge intersect if they share an edge. The cliques of an EPT graph are characterized and shown to have strong Helly number 4. From this it is demonstrated that the problem of finding a maximum clique of an EPT graph can be solved in polynomial time. It is shown that the strong p...
متن کاملDefining Fairness
We propose a definition for the class of all fairness properties of a given system. We provide independent characterizations in terms of topology, language theory and game theory. All popular notions of fairness from the literature satisfy our definition. Moreover our class is closed under union and countable intersection, and it is, in a sense, the maximal class having this property. On the wa...
متن کاملRecognizing large-degree Intersection Graphs of Linear 3-Uniform Hypergraphs
The intersection graph or the line graph Ω(H) of a hypergraph H is defined as follows: 1) the vertices of Ω(H) are in a bijective correspondence with the edges of H, 2) two vertices are adjacent in Ω(H) if and only if the corresponding edges intersect. Characterizing and recognizing intersection graphs of hypergraphs with some additional property P is one of the central problems in intersection...
متن کاملColoring intersection graphs of x-monotone curves in the plane
A class of graphs G is χ-bounded if the chromatic number of the graphs in G is bounded by some function of their clique number. We show that the class of intersection graphs of simple families of x-monotone curves in the plane intersecting a vertical line is χ-bounded. As a corollary, we show that the class of intersection graphs of rays in the plane is χ-bounded, and the class of intersection ...
متن کامل4 J an 2 00 6 Intersection numbers with Witten ’ s top Chern class Sergei Shadrin
Witten’s top Chern class is a particular cohomology class on the moduli space of Riemann surfaces endowed with r-spin structures. It plays a key role in Witten’s conjecture relating to the intersection theory on these moduli spaces. Our first goal is to compute the integral of Witten’s class over the so-called double ramification cycles in genus 1. We obtain a simple closed formula for these in...
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 2004