Topic
Divisor
About: Divisor is a research topic. Over the lifetime, 2462 publications have been published within this topic receiving 21394 citations. The topic is also known as: factor & submultiple.
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01 Jan 2012
TL;DR: The Chern class of logarithmic derivations along a simple normal crossing divisor equals the Chern-Schwartz-MacPherson class of the complement of the divisors as discussed by the authors.
Abstract: The Chern class of the sheaf of logarithmic derivations along a simple normal crossing divisor equals the Chern-Schwartz-MacPherson class of the complement of the divisor. We extend this equality to more general divisors, which are locally analytically isomorphic to free hyperplane arrangements.
1 citations
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TL;DR: In this paper, it was shown that for each fixed natural number m, there exist computable constants el, e z,..., era, fa,f2..... fro, 0 2).
Abstract: and as usual co(n) is the number of distinct prime factors of n, f2(n) is the total number of prime factors of n, f II n means that p~ (p prime) exactly divides n. It was shown in [1] that, for each fixed natural number m, there exist computable constants el, e z, ..., era, fa,f2 ..... fro, 0 2). These questions were considered in a general setting by De Koninck and Mercier [2], where under suitable conditions asymptotic relations of the form (1.3) Y~ f(P(n)) = (1 + o(1)) Z f(n) (x ~co)
1 citations
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TL;DR: In this paper, the authors give an overview of combinatoric properties of the number of ordered factorizations of an integer, where every factor is greater or equal to 2, and give explicit expressions for the degree and coefficients of this polynomial.
Abstract: We give an overview of combinatoric properties of the number of ordered $k$-factorizations $f_k(n,l)$ of an integer, where every factor is greater or equal to $l$. We show that for a large number $k$ of factors, the value of the cumulative sum $F_k(x,l)=\sum
olimits_{n\leq x} f_k(n,l)$ is a polynomial in $\lfloor \log_l x \rfloor$ and give explicit expressions for the degree and the coefficients of this polynomial. An average order of the number of ordered factorizations for a fixed number $k$ of factors greater or equal to 2 is derived from known results of the divisor problem.
1 citations
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TL;DR: In this article, the pullback of the Mukai symplectic form on moduli spaces of stable sheaves over a K3 or abelian surface X is shown to coincide with a holomorphic 2-form on the Hilbert scheme.
Abstract: Fix a smooth very ample curve C on a K3 or abelian surface X. Let $ \mathcal{M} $ denote the
moduli space of pairs of the form (F, s), where F is a stable sheaf over X whose Hilbert polynomial
coincides with that of the direct image, by the inclusion map of C in X, of a line bundle of degree d
over C, and s is a nonzero section of F. Assume d to be sufficiently large such that F has a nonzero
section. The pullback of the Mukai symplectic form on moduli spaces of stable sheaves over X is
a holomorphic 2-form on $ \mathcal{M} $. On the other hand, $ \mathcal{M} $ has a map to a Hilbert scheme parametrizing
0-dimensional subschemes of X that sends (F, s) to the divisor, defined by s, on the curve defined
by the support of F. We prove that the above 2-form on $ \mathcal{M} $ coincides with the pullback of the
symplectic form on the Hilbert scheme.
1 citations