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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TL;DR: In this article, the wobbly locus of semi-stable vector bundles admits a non-zero nilpotent Higgs field is shown to be a union of divisors.
Abstract: Let $X$ be a smooth projective complex curve of genus $g \geq 2$ and let $\M_X(2,\Lambda)$ be the moduli space of semi-stable rank-$2$ vector bundles over $X$ with fixed determinant $\Lambda$. We show that the wobbly locus, i.e., the locus of semi-stable vector bundles admitting a non-zero nilpotent Higgs field is a union of divisors $\Ww_k \subset \M_X(2,\Lambda)$. We show that on one wobbly divisor the set of maximal subbundles is degenerate. We also compute the class of the divisors $\Ww_k$ in the Picard group of $\M_X(2,\Lambda)$.
14 citations
TL;DR: When q is odd or d is even, it is found that relative difference sets with these parameters exist if and only if n is a divisor of q?1.
14 citations
Patent•
01 Aug 1995TL;DR: An ink-jet printer that prints using an interlace ratio of higher than 2:1 can be found in this paper, where the print head has an internozzle spacing of N, while the inter-lace ratio n:1 is selected so that n is an integer divisor of N+2 or N+4 or is equal to N+1.
Abstract: An ink-jet printer that prints using an interlace ratio of higher than 2:1 The print head has an internozzle spacing of N, while the interlace ratio n:1 is selected so that n is an integer divisor of N+2 or N+4 or is equal to N+1 Multiple interlaced images can be "stitched" together by printing a first interlaced image, moving the print head and printing a second interlaced image such that the head of the second image overlaps with the tail of the first interlaced image
14 citations
TL;DR: In this article, it was shown that as x approaches ∞, #{n ≤ x: d(n) divides n} = ( x √ log x)( log log x) −1 + 0(1).
14 citations
01 Jan 1994
TL;DR: In this paper, the problem of enumerative geometry of the vector bundle of rank d over H d has been studied in the context of the description of the smooth structure of the 4-manifold underlying a smooth algebraic surface.
Abstract: Let S be a smooth irreducible algebraic surface over ℂ, H d a Hilbert scheme of 0-dimensional subschemes of length d in S, dim H d = 2d, and Z d ⊂ S × H d a universal family with natural projections \(S\xleftarrow{{{\tau _d}}}{Z_d}\xrightarrow{{{\pi _d}}}{H_d}\). Fix an arbitrary divisor D on S and denote \(\varepsilon _D^d = {\pi _{d*}}\tau _d^*{O_S}(D)\). Since π d is a flat finite morphism of degree d, the sheaf e D d is in fact the vector bundle of rank d over H d . We call e D d the standard vector bundle over H d . The problem of computation of its Segre classes is connected with a number of questions of enumerative geometry. In recent times it has got applications to the description of the smooth structure of the 4-manifold underlying S — see [10].
14 citations