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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars:Recent developments on random hyperbolic surfaces of large genus
大属随机 双曲曲面 球面几何
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2023/4/21
A Desingularization of the Main Component of the Moduli Space of Genus-One Stable Maps into P n
Genus-One Stable Maps Moduli
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2015/7/14
We construct a natural smooth compactication of the space of smooth genus-one curves with
k distinct points in a projective space. It can be viewed as an analogue of a well-known smooth
compactica...
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...
PRIME SPECIALIZATION IN HIGHER GENUS II
Bateman–Horn conjecture Hardy–Littlewood conjecture
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2015/7/6
We continue the development of the theory of higher-genus M¨obius periodicity
that was studied in Part I for odd characteristic, now treating asymptotic questions and
the case of characteristic 2. T...
Semi-ordinary p-stabilization of the Siegel Eisenstein series of arbitrary genus
Siegel modular forms Eisenstein series p-adic analytic family
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2012/7/11
For a given odd prime p, we define a certain p-stabilization of the Siegel Eisenstein series of arbitrary genus so that the resulting eigenvalue of a generalized Atkin operator at p is a p-adic unit (...
Local invariants on quotient singularities and a genus formula for weighted plane curves
Local invariants quotient singularities genus formula weighted plane curves Algebraic Geometry
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2012/6/30
In this paper we extend the concept of Milnor fiber and Milnor number of a curve singularity allowing the ambient space to be a quotient surface singularity. A generalization of the local {\delta}-inv...
The minimal genus problem for elliptic surfaces
4-manifold elliptic surface diffeomorphism group minimal genus
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2012/6/25
We partly solve the minimal genus problem for embedded surfaces in the case of elliptic 4-manifolds. This involves a certain restricted transitivity property of the action of the orientation preservin...
Obtaining genus 2 Heegaard splittings from Dehn surgery
genus 2 Heegaard splittings Dehn surgery Geometric Topology
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2012/5/9
Let K' be a hyperbolic knot in S^3 and suppose that some Dehn surgery on K' with distance at least 3 from the meridian yields a 3-manifold M of Heegaard genus 2. We show that if M does not contain an ...
Pairing-based algorithms for jacobians of genus 2 curves with maximal endomorphism ring
Pairing-based algorithms jacobians of genus 2 curves maximal endomorphism ring Number Theory
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2012/4/17
Using Galois cohomology, Schmoyer characterizes cryptographic non-trivial self-pairings of the $\ell$-Tate pairing in terms of the action of the Frobenius on the $\ell$-torsion of the Jacobian of a ge...
Separating Curve Complex of the Genus Two Surface is Hyperbolic
Curve Complex the Genus Two Surface Hyperbolic Geometric Topology
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2011/9/8
Abstract: A proof that the separating curve complex of the closed genus two surface has a quasi-distance formula and is delta hyperbolic using tools of Masur and Schleimer. This answers in the affirma...
Cosmetic crossings of genus one knots
cosmetic crossing nugatory crossing Thurston norm pretzel knot Whitehead double
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2011/9/1
Abstract: We show that for genus one knots the Alexander polynomial and the homology of the double cover branching over the knot provide obstructions to cosmetic crossings. As an application we prove ...
The Gieseker-Petri divisor in M_g for genus g<=13
Gieseker-Petri divisor M_g for genus g<=13
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2011/1/21
The Gieseker-Petri locus GPg is defined as the locus insideMg consisting of curves which violate the Gieseker-Petri Theorem. It is known that GPg has always some divisorial components and it has been ...
On genus-1 simplified broken Lefschetz fibrations
genus-1 simplified Lefschetz fibrations
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2011/2/22
Auroux, Donaldson and Katzarkov introduced broken Lefschetz fibrations as a generalization of Lefshcetz fibrations in order to describe near-symplectic 4-manifolds.We first study monodromy representat...
The rationality of the moduli spaces of trigonal curves of odd genus
trigonal curve rationality of moduli
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2011/1/18
The moduli spaces of trigonal curves of odd genus g ≥ 5 are proven to be rational.