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Let $G$ be a finite abelian group acting faithfully on ${\mathbb C}{\mathbb P}^1$ via holomorphic automorphisms. In \cite{DF2} the $G$--equivariant algebraic vector bundles on $G$--invariant affine open subsets of ${\mathbb C}{\mathbb P}^1$ were clas
Externí odkaz:
http://arxiv.org/abs/2406.03926
Given a singular connection $D$ on a vector bundle $E$ over an irreducible smooth projective curve $X$, defined over an algebraically closed field, we show that there is a unique maximal subsheaf of $E$ on which $D$ induces a nonsingular connection.
Externí odkaz:
http://arxiv.org/abs/2301.03813
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Let $M$ be a compact connected complex manifold and $G$ a connected reductive complex affine algebraic group. Let $E_G$ be a holomorphic principal $G$--bundle over $M$ and $T\, \subset\, G$ a torus containing the connected component of the center of
Externí odkaz:
http://arxiv.org/abs/1906.05364
Let $\varphi : Y \rightarrow X$ be a finite surjective morphism between smooth complex projective curves, where $X$ is irreducible but $Y$ need not be so. Let $V_*$ be a parabolic vector bundle on $Y$. We construct a parabolic structure on the direct
Externí odkaz:
http://arxiv.org/abs/1810.06752
Autor:
Machu, Francois Xavier
We define the Gromov-Witten invariants for the parabolic bundles over an orbifold $C$ in various situation. Those bring us to refine this notion to get an accurate computation of the number of maximal subbundles of a sufficiently general parabolic bu
Externí odkaz:
http://arxiv.org/abs/1410.2448
Autor:
Machu, Francois-Xavier
We investigate the Shioda-Inose structure of the Jacobian of a smooth complex genus-2 curve C arising from its degree-2 elliptic subcovers and determine the Mordell-Weil groups and lattices in the case of a semistable fibration having exactly four si
Externí odkaz:
http://arxiv.org/abs/1409.4950
Autor:
Machu, François Xavier1 (AUTHOR), Wang, Ru Julie1 (AUTHOR), Cheng, Jean Louis1 (AUTHOR), Cocks, Jeremy1 (AUTHOR), Wang, Qiuping Alexandre1,2 (AUTHOR) alexandre.wang@univ-lemans.fr
Publikováno v:
Entropy. Feb2023, Vol. 25 Issue 2, p305. 8p.
Autor:
Machu, Francois-Xavier
We construct the Kuranishi spaces, or in other words, the versal deformations, for the following classes of connections with fixed divisor of poles $D$: all such connections, as well as for its subclasses of integrable, integrable logarithmic and int
Externí odkaz:
http://arxiv.org/abs/1009.1898
Autor:
Machu, Francois-Xavier
We provide a sketch of the GIT construction of the moduli spaces for the three classes of connections: the class of meromorphic connections with fixed divisor of poles $D$ and its subclasses of integrable and integrable logarithmic connections. We us
Externí odkaz:
http://arxiv.org/abs/1009.1899