An intersection number for the punctual Hilbert scheme of a surface
نویسندگان
چکیده
منابع مشابه
Intersection theory on punctual Hilbert schemes and graded Hilbert schemes
The rational Chow ring A(S,Q) of the Hilbert scheme S parametrising the length n zero-dimensional subschemes of a toric surface S can be described with the help of equivariant techniques. In this paper, we explain the general method and we illustrate it through many examples. In the last section, we present results on the intersection theory of graded Hilbert schemes.
متن کاملGröbner Strata in the Punctual Hilbert Scheme
Given a standard set δ of a finite size r, we show that the functor associating to a k-algebra B the set of all reduced Gröbner bases with standard set δ is representable. We show that the representing scheme Hilb′ δ k[x]/k is a locally closed stratum in the punctual Hilbert scheme Hilbrk[x]/k. Moreover, we cover the punctual Hilbert scheme by open affine subschemes attached to all standard set...
متن کاملOn the punctual Hilbert scheme of a symplectic fourfold
which to a subscheme associates its cycle that is its support together with the local multiplicities makes it a desingularization of the symmetric product S k The morphism c is an isomorphism over the Zariski open set S k parametrizing k uples of distinct points so that Hilbk S is as well a smooth partial compacti cation of S k which is compact when S is compact The ber c z z S k is a singular ...
متن کاملThe Full Flag Hilbert Scheme of Nodal Curves and the Punctual Hilbert Scheme of Points of the Cusp Curve.
We study the relative full-flag Hilbert scheme of a family of curves, parameterizing chains of subschemes, containing a node. We will prove that the relative full flag Hilbert scheme is normal with locally complete intersection singularities. We also study the Hilbert scheme of points of the cusp curve and show the punctual Hilbert scheme is isomorphic to P. We will see the Hilbert scheme has o...
متن کاملSome lower bounds for the $L$-intersection number of graphs
For a set of non-negative integers~$L$, the $L$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $A_v subseteq {1,dots, l}$ to vertices $v$, such that every two vertices $u,v$ are adjacent if and only if $|A_u cap A_v|in L$. The bipartite $L$-intersection number is defined similarly when the conditions are considered only for the ver...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1998
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-98-01972-2