HIRZEBRUCH χy GENERA OF THE HILBERT SCHEMES OF SURFACES BY LOCALIZATION FORMULA
نویسندگان
چکیده
We use the Atiyah-Bott-Berline-Vergne localization formula to calculate the Hirzebruch χy genus χy(S), where S[n] is the Hilbert schemes of points of length n of a surface S. Combinatorial interpretation of the weights of the fixed points of the natural torus action on (C2)[n] is used.
منابع مشابه
CALCULATIONS OF THE HIRZEBRUCH χy GENERA OF SYMMETRIC PRODUCTS BY THE HOLOMORPHIC LEFSCHETZ FORMULA
We calculate the Hirzebruch χy andˆχy-genera of symmetric products of closed complex manifolds by the holomorphic Lefschetz formula of Atiyah and Singer [4]. Such calculation rederive some formulas proved in an earlier paper [14] by a different method. Let M be a smooth manifold, and G a finite group of diffeomorphisms. There are two kinds of interesting cohomology theories for the orbifold M/G...
متن کاملA path integral derivation of χy-genus
The formula for the Hirzebruch χy-genus of complex manifolds is a consequence of the Hirzebruch–Riemann–Roch formula. The classical index formulae for Todd genus, Euler number and signature correspond to the case when the complex variable y = 0,−1 and 1 respectively. Here we give a direct derivation of this nice formula based on supersymmetric quantum mechanics. PACS numbers: 12.60.Jv, 02.40.Ma...
متن کاملm at h . A T ] 1 3 Fe b 20 07 HODGE GENERA OF ALGEBRAIC VARIETIES , II
We study the behavior of Hodge-theoretic genera under morphisms of complex algebraic varieties. We prove that the additive χy-genus which arises in the motivic context satisfies the so-called “stratified multiplicative property”, which shows how to compute the invariant of the source of a proper surjective morphism from its values on various varieties that arise from the singularities of the ma...
متن کاملSegre Classes and Hilbert Schemes of Points
We prove a closed formula for the integrals of the top Segre classes of tautological bundles over the Hilbert schemes of points of a K3 surface X. We derive relations among the Segre classes via equivariant localization of the virtual fundamental classes of Quot schemes on X. The resulting recursions are then solved explicitly. The formula proves the K-trivial case of a conjecture of M. Lehn fr...
متن کاملOn Families of Rank-2 Uniform Bundles on Hirzebruch Surfaces and Hilbert Schemes of Their Scrolls
Several families of rank-two vector bundles on Hirzebruch surfaces are shown to consist of all very ample, uniform bundles. Under suitable numerical assumptions, the projectivization of these bundles, embedded by their tautological line bundles as linear scrolls, are shown to correspond to smooth points of components of their Hilbert scheme, the latter having the expected dimension. If e = 0, 1...
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 2000