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RECURSIONS FOR CHARACTERISTIC NUMBERS OF GENUS ONE PLANE CURVES
CHARACTERISTIC PLANE CURVES
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2015/7/14
Characteristic numbers of families of maps of nodal curves to P2 are dened as
intersection of natural divisor classes. (This denition agrees with the usual denition for
families of plane curves.)...
GENUS 0 AND 1 HURWITZ NUMBERS: RECURSIONS, FORMULAS, AND GRAPH-THEORETIC INTERPRETATIONS
RECURSIONS FORMULAS GRAPH-THEORETIC
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2015/7/14
We derive a closed-form expression for all genus 1 Hurwitz numbers, and give a
simple new graph-theoretic interpretation of Hurwitz numbers in genus 0 and 1. (Hurwitz
numbers essentially count irred...
ON ADDING A LIST OF NUMBERS (AND OTHER ONE-DEPENDENT DETERMINANTAL PROCESSES)
Add list of Numbers the determinant processes
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2015/7/8
ON ADDING A LIST OF NUMBERS (AND OTHER ONE-DEPENDENT DETERMINANTAL PROCESSES)。
ROOT NUMBERS AND RANKS IN POSITIVE CHARACTERISTIC
POSITIVE CHARACTERISTIC ROOT NUMBERS
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2015/7/6
Inspired by this, for the rational
function field K = κ(u) over any finite field κ with characteristic 6= 2, we construct an
explicit 2-parameter family Ec,d of non-isotrivial elli...
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No strength in numbers(图)
numbers No strength
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2014/3/21
Urban legislators have long lamented that they do not get their fair share of bills passed in state governments, often blaming rural and suburban interests for blocking their efforts. Now, a new study...
Generalization of Proth's and Miller's theorems for $Kp^n+1$ numbers
Proth's Miller's theorems
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2010/11/24
In this paper we generalize classical results by Miller and Proth for integers of the form $N=Kp^n+1$. The first generalization of Proth's theorem requires the use of a base which is a $p$-th power n...
Arc numbers from Gauss diagrams
Arc numbers Gauss diagrams
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2010/11/8
We characterize planar diagrams which may be divided into n arc embeddings in terms of their chord diagrams, generalizing a result of Taniyama for the case n = 2. Two algorithms are provided, one whi...
Integrality of L2-Betti numbers
Integrality L2-Betti numbers
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2010/10/29
The Atiyah conjecture predicts that the L2-Betti numbers of a finite CW-complex with torsion-free fundamental group are integers. We show that the Atiyah conjecture holds (with an additional technica...
Drawing with Complex Numbers
Drawing Complex Numbers
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2010/10/29
It is not commonly realized that the algebra of complex numbers can be used in an elegant way to represent the images of ordinary 3-dimensional figures, orthographically projected to the plane. We de...
Simple Divisibility Rules for the 1st 1000 Prime Numbers
Simple Divisibility Rules 1st 1000 Prime Numbers
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2010/10/29
Simple divisibility rules are given for the 1st 1000 prime numbers.