Characteristic numbers of algebraic varieties.
نویسنده
چکیده
A rational linear combination of Chern numbers is an oriented diffeomorphism invariant of smooth complex projective varieties if and only if it is a linear combination of the Euler and Pontryagin numbers. In dimension at least 3, only multiples of the top Chern number, which is the Euler characteristic, are invariant under diffeomorphisms that are not necessarily orientation preserving. In the space of Chern numbers, there are 2 distinguished subspaces, one spanned by the Euler and Pontryagin numbers, and the other spanned by the Hirzebruch-Todd numbers. Their intersection is the span of the Euler number and the signature.
منابع مشابه
Characteristic Numbers, Genera, and Resolutions
In this paper we survey various constructions and properties of genera and characteristic numbers of singular complex algebraic varieties. In particular, we discuss genera for the singular varieties appearing in the minimal model program, as well as those defined by Hodge theory and functorial characteristic classes.
متن کاملAlgorithmic Computation of Local Cohomology Modules and the Cohomological Dimension of Algebraic Varieties
In this paper we present algorithms that compute certain local cohomology modules associated to a ring of polynomials containing the rational numbers. In particular we are able to compute the local cohomological dimension of algebraic varieties in characteristic zero.
متن کاملDivisibility of characteristic numbers
We use homotopy theory to define certain rational coefficients characteristic numbers with integral values, depending on a given prime number q and positive integer t . We prove the first nontrivial degree formula and use it to show that existence of morphisms between algebraic varieties for which these numbers are not divisible by q give information on the degree of such morphisms or on zero c...
متن کاملBounding the equivariant Betti numbers and computing the generalized Euler-Poincaré characteristic of symmetric semi-algebraic sets
Unlike the well known classical bounds due to Oleinik and Petrovskii, Thom and Milnor on the Betti numbers of (possibly non-symmetric) real algebraic varieties and semialgebraic sets, the above bound is polynomial in k when the degrees of the defining polynomials are bounded by a constant. Moreover, our bounds are asymptotically tight. As an application we improve the best known bound on the Be...
متن کاملCharacteristics of Algebraic Varieties Sylvain
The aim of this note is to study the behavior of intersection homology Euler characteristic under morphisms of algebraic varieties. The main result is a direct application of the BBDG decomposition theorem. Similar formulae for Hodge-theoretic invariants of algebraic varieties were announced by the first and third authors in [4, 11].
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:
- Proceedings of the National Academy of Sciences of the United States of America
دوره 106 25 شماره
صفحات -
تاریخ انتشار 2009