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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.
DELIGNE PAIRINGS AND FAMILIES OF RANK ONE LOCAL SYSTEMS ON ALGEBRAIC CURVES
DELIGNE PAIRINGS LOCAL SYSTEMS ALGEBRAIC CURVES
2015/12/17
For smooth families of projective algebraic curves, we extend the notion of intersection pairing of metrized line bundles to a pairing on line bundles with flat relative connections. In this setting, ...
Approximate Parametrization of Space Algebraic Curves
Approximate Parametrization Space Algebraic Curves Algebraic Geometry
2011/8/30
Abstract: Given a non-rational real space curve and a tolerance $\epsilon>0$, we present an algorithm to approximately parametrize the curve. The algorithm checks whether a planar projection of the sp...
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.
Birkhoff strata of the Grassmannian Gr$\mathrm{^{(2)}}$: Algebraic curves
Birkhoff strata the Grassmannian
2010/11/23
Algebraic varieties and curves arising in Birkhoff strata of the Sato Grassmannian Gr${^{(2)}}$ are studied. It is shown that the big cell $\Sigma_0$ contains the tower of families of the normal rati...
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
In this paper, we develop the theory of flashes of an algebraic curve. We show that the theory is birationally invariant in a sense which we will make more precise below. We also show how the theory p...
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...
Rational quadratic approximation to real algebraic curves
Real algebraic curve Parametrization Approximation Topology determination
2013/9/9
An algorithm is proposed to give a global approximation of an implicit real plane algebraic curve with rational quadratic B-spline curves. The algorithm consists of four steps: topology determination,...
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...