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 paper, the Gromov-Witten type invariants for stable sheaves were calculated by virtue of Euler numbers of some moduli spaces of stable sheaving.
Abstract: Let X be a K3 surface with a primitive ample divisor H, and let $\beta=2[H]\in H_2(X, \mathbf Z)$. We calculate the Gromov-Witten type invariants $n_{\beta}$ by virtue of Euler numbers of some moduli spaces of stable sheaves. Eventually, it verifies Yau-Zaslow formula in the non primitive class $\beta$.
7 citations
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TL;DR: In this article, the authors derived the modified Belov-Chaltikian lattice hierarchy associated with a discrete 3×3 matrix spectral problem and derived a tri gonal curve Km−2 of arithmetic genus m−2.
Abstract: Using the Lenard recurrence relations and the zero-curvature equation, we derive the modified Belov—Chaltikian lattice hierarchy associated with a discrete 3×3 matrix spectral problem. Using the characteristic polynomial of the Lax matrix for the hierarchy, we introduce a tri gonal curve Km−2 of arithmetic genus m−2. We study the asymptotic properties of the Baker—Akhiezer function and the algebraic function carrying the data of the divisor near $$P_{\infty_{1}}$$
, $$P_{\infty_{2}}$$
, $$P_{\infty_{3}}$$
, and P0 on Km−2. Based on the theory of trigonal curves, we obtain the explicit theta-function representations of the algebraic function, the Baker—Akhiezer function, and, in particular, solutions of the entire modified Belov—Chaltikian lattice hierarchy.
7 citations
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TL;DR: In this article, it was shown that the moduli space of genus g stable hyperelliptic curves with $n$ marked points has non-negative Kodaira dimension for n = 4g+6.
Abstract: It is known that the moduli space $\overline{\mathcal{H}}_{g,n}$ of genus g stable hyperelliptic curves with $n$ marked points is uniruled for $n \geq 4g+5$. In this paper we consider the complementary case and show that $\overline{\mathcal{H}}_{g,n}$ has non-negative Kodaira dimension for $n = 4g+6$ and is of general type for $n \geq 4g+7$. Important parts of our proof are the calculation of the canonical divisor and establishing that the singularities of $\overline{\mathcal{H}}_{g,n}$ do not establish adjunction conditions.
7 citations
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TL;DR: In this article, it was shown that such an inequality does not hold anymore with d = 1/n and sufficiently small $c. The result of Gross and Vincent was generalized to values of binary forms and decomposable forms at integral points.
Abstract: Let $S$ be a finite set of primes. The $S$-part $[m]_S$ of a non-zero integer $m$ is the largest positive divisor of $m$ that is composed of primes from $S$. In 2013, Gross and Vincent proved that if $f(X)$ is a polynomial with integer coefficients and with at least two roots in the complex numbers, then for every integer $x$ at which $f(x)$ is non-zero, we have (*) $[f(x)]_S\leq c\cdot |f(x)|^d$, where $c$ and $d$ are effectively computable and $d 1/n$, provided we do not require effectivity of $c$. Further, we show that such an inequality does not hold anymore with $d=1/n$ and sufficiently small $c$. In addition we prove a density result, giving for every $\epsilon>0$ an asymptotic estimate with the right order of magnitude for the number of integers $x$ with absolute value at most $B$ such that $f(x)$ has $S$-part at least $|f(x)|^{\epsilon}$. The result of Gross and Vincent, as well as the other results mentioned above, are generalized to values of binary forms and decomposable forms at integral points. Our main tools are Baker type estimates for linear forms in complex and $p$-adic logarithms, the $p$-adic Subspace Theorem of Schmidt and Schlickewei, and a recent general lattice point counting result of Barroero and Widmer.
7 citations
01 Jan 2013
TL;DR: The divisor theory for graphs is compared to the theory of linear series on curves through the correspondence associating a curve to its dual graph as mentioned in this paper, and an algebro-geometric interpretation of the combinatorial rank is pro-posed, and proved in some cases.
Abstract: The divisor theory for graphs is compared to the theory of linear series on curves through the correspondence associating a curve to its dual graph. An algebro-geometric interpretation of the combinatorial rank is pro- posed, and proved in some cases.
6 citations