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School Colloquium——Stable reduction of algebraic curves and abelian varieties
北大 algebraic curves abelian varieties
2023/6/16
The stable reduction theorem was proved by Grothendieck for Abelian varieties and subsequently by Deligne and Mumford for projective curves.
Schur function expansions of KP tau functions associated to algebraic curves
Schur function expansions of KP tau functions algebraic curves
2010/12/28
The Schur function expansion of Sato-Segal-Wilson KP τ -functions is reviewed. The case of
τ -functions related to algebraic curves of arbitrary genus is studied in detail. Explicit expressions for t...
Schur function expansions of KP tau functions associated to algebraic curves
Schur function expansions of KP tau functions algebraic curves
2011/2/21
The Schur function expansion of Sato-Segal-Wilson KP τ -functions is reviewed. The case of
τ -functions related to algebraic curves of arbitrary genus is studied in detail.
Irreducibility of the space of cyclic covers of algebraic curves of fixed numerical type and the irreducible components of $Sing (\bar{\mathfrak M_g})$
space algebraic curves numerical type irreducible components
2010/11/8
We prove irreducibility for the space of cyclic covers of fixed numerical type between smooth projective curves, and also for the space of cyclic covers of prime order and of fixed numerical-combinato...
Analytic continuation of functions along parallel algebraic curves
Analytic continuation functions along parallel algebraic curves
2010/11/11
In this work we study a problem about analytic continuation along parallel algebraic curves
For any d\ge 5, I constructed infinitely many pairwise smoothly non-equivalent surfaces F\subset\Cp{2} homeomorphic to a non-singular algebraic curve of degree d, realizing the same homology class as ...
We use a combination of both algebraic and numerical
techniques to construct a $C^1$-continuous, piecewise $(m,n)$
rational $\epsilon$-approximation of a real algebraic plane curve of
degree $d$.
...
ON THE ISOMORPHISMS OF SMOOTH ALGEBRAIC CURVES (Ⅰ)
Algebraic curve isomorphism genus canoni
2007/8/7
In this paper, I have considered some problems of algebraic curves in some constructive way, especially, I give an algorithm for determining whether two given smooth plane curves are isomorphic and fi...
On the Parameterization of Algebraic Curves
Computer modeling parameterization surface intersections algebraic curves resolvents Ritt{Wu's decomposition algorithm GrAobner bases
2013/9/9
In this paper, by using the concept of resolvents of a prime ideal introduced by Ritt, we give methods for constructing a hypersurface which is birational to a given irreducible variety and birational...