WebThe Chow scheme parameterizes one-dimensional cycles Z of 3 degree two on P . It is connected and has two irreducible components. One of these parameterizes conics contained in a plane and lines of multiplicity two. The other com- ponent parameterizes pairs of skew lines, singular conics and lines of multiplicity two. WebApr 1, 2024 · Class of the graph of the Segre embedding in the Chow ring (Eisenbud & Harris, 3264 and all that, Exercise 2.26) 2 Generically reduced preimage implies generically transverse intersection
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Webthe usual (absolute) Chow groups, particularly those that relate the Chow groupsto algebraic K-theory. 1.1. Let Xbe a regular scheme essentially of finite type over a field k. (Regularity can be relaxed in muchofwhat follows.) Wehave the following invariants: zm(x),thegroupofcodimension-p algebraiccycles on X.Thatis, zm(x) WebLet L be a line bundle on a scheme X. For any k-dimensionsal subvariety V of X, the restriction Lj V of L to V is isomorphic to O V(C) for some Cartier divisor C on V. The Weil divisor [C] determines a well-defined element in A k 1(X) which we denote by c 1(L)\V. We extend this map linearly to get the 1st Chern class c 1(L)\: A k(X) !A k 1(X). intuition painting
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WebApr 1, 2024 · Understanding the proof of the fact that the Chow group of a scheme X is graded by dimension. Ask Question Asked 4 years ago Modified 4 years ago Viewed 96 … WebFor a general regular scheme X, X Xwill not be regular, and the diago-nal map X!X Xwill not be a regular immersion. Hence we cannot use deformation to the normal cone to construct a product on the Chow groups. In SGA6, [2], Grothendieck and his collaborators showed that, when Xis regular CH(X) Q’Gr (K 0(X)) Webscheme structure de ned by the Jacobian ideal of X(we will say then that Y is the singular scheme of X, to emphasize that the scheme structure of Y is important for our considerations). In this note we consider a class in the Chow group of Y which arises naturally in this setup, and which captures much intersection-theoretic newport ri to sandwich ma