Masa-Hiko Saito
Masa-Hiko Saito has a total of 8 co-authors. Here are the top co-authors by number of shared publications:
- Arata Komyo
University of Hyogo, Hyogo, Japan
3 shared publications - Frank Loray
Univ Rennes CNRS IRMAR -UMR 6625 F-35000 Rennes France
3 shared publications - Szilárd Szabó
Department of Algebra and Geometry Institute of Mathematics Faculty of Natural Sciences Budapest University of Technology and Economics Műegyetem rkp. 3. Bu- dapest H-1111 Hungary
2 shared publications - Arata Komyo
© Université Paul Sabatier, Toulouse, 2021
1 shared publication - Indranil Biswas
Department of Mathematics, Shiv Nadar University, Greater Noida, India
1 shared publication - Michi-Aki Inaba1 shared publication
Latest Publications
- Open Access
Applications of the Liouville symplectic form on the cotangent bundle of a loop group
Let $G$ be a semisimple, simply connected, affine algebraic group defined over $\mathbb C$. Consider the Liouville symplectic structure on the total space $T^*G((t))$ of the cotangent bundle of the loop group $G((t))$, where $t$ is a formal parameter. We show that the Liouville symplectic structure on $T^*G((t))$ induces the symplectic structures on the moduli stack of framed principal Higgs $G$-bundles on a compact connected Riemann surface $X$ and also on the moduli spaces of framed $G$-connections on $X$. Similar symplectic structures -- on the moduli stack of framed principal Higgs $G$-bundles, with finite order framing, and also framed connections on $X$, with finite order framing -- were constructed earlier by various authors. Our results show that they all have a common origin.Open AccessApplications of the Liouville symplectic form on the cotangent bundle of a loop group
Let $G$ be a semisimple, simply connected, affine algebraic group defined over $\mathbb C$. Consider the Liouville symplectic structure on the total space $T^*G((t))$ of the cotangent bundle of the loop group $G((t))$, where $t$ is a formal parameter. We show that the Liouville symplectic structure on $T^*G((t))$ induces the symplectic structures on the moduli stack of framed principal Higgs $G$-bundles on a compact connected Riemann surface $X$ and also on the moduli spaces of framed $G$-connections on $X$. Similar symplectic structures -- on the moduli stack of framed principal Higgs $G$-bundles, with finite order framing, and also framed connections on $X$, with finite order framing -- were constructed earlier by various authors. Our results show that they all have a common origin. - Open Access
Canonical coordinates for moduli spaces of rank two irregular connections on curves
In this paper, we study a geometric counterpart of the cyclic vector which allow us to put a rank 2 meromorphic connection on a curve into a ``companion'' normal form. This allow us to naturally identify an open set of the moduli space of $\mathrm{GL}_2$-connections (with fixed generic spectral data, i.e. unramified, non resonant) with some Hilbert scheme of points on the twisted cotangent bundle of the curve. We prove that this map is symplectic, therefore providing Darboux (or canonical) coordinates on the moduli space, i.e. separation of variables. On the other hand, for $\mathrm{SL}_2$-connections, we give an explicit formula for the symplectic structure for a birational model given by Matsumoto. We finally detail the case of an elliptic curve with a divisor of degree $2$.Open AccessCanonical coordinates for moduli spaces of rank two irregular connections on curves
In this paper, we study a geometric counterpart of the cyclic vector which allow us to put a rank 2 meromorphic connection on a curve into a ``companion'' normal form. This allow us to naturally identify an open set of the moduli space of $\mathrm{GL}_2$-connections (with fixed generic spectral data, i.e. unramified, non resonant) with some Hilbert scheme of points on the twisted cotangent bundle of the curve. We prove that this map is symplectic, therefore providing Darboux (or canonical) coordinates on the moduli space, i.e. separation of variables. On the other hand, for $\mathrm{SL}_2$-connections, we give an explicit formula for the symplectic structure for a birational model given by Matsumoto. We finally detail the case of an elliptic curve with a divisor of degree $2$. - Open Access
Canonical coordinates for moduli spaces of rank two irregular connections on curves.
In this paper, we study a geometric counterpart of the cyclic vector which allow us to put a rank 2 meromorphic connection on a curve into a “companion” normal form. This allow us to naturally identify an open set of the moduli space of GL2-connections (with fixed generic spectral data, i.e. unramified, non resonant) with some Hilbert scheme of points on the twisted cotangent bundle of the curve. We prove that this map is symplectic, therefore providing Darboux (or canonical) coordinates on the moduli space, i.e. separation of variables. On the other hand, for SL2-connections, we give an explicit formula for the symplectic structure for a birational model given by Matsumoto. We finally detail the case of an elliptic curve with a divisor of degree 2.
Open AccessCanonical coordinates for moduli spaces of rank two irregular connections on curves.
In this paper, we study a geometric counterpart of the cyclic vector which allow us to put a rank 2 meromorphic connection on a curve into a “companion” normal form. This allow us to naturally identify an open set of the moduli space of GL2-connections (with fixed generic spectral data, i.e. unramified, non resonant) with some Hilbert scheme of points on the twisted cotangent bundle of the curve. We prove that this map is symplectic, therefore providing Darboux (or canonical) coordinates on the moduli space, i.e. separation of variables. On the other hand, for SL2-connections, we give an explicit formula for the symplectic structure for a birational model given by Matsumoto. We finally detail the case of an elliptic curve with a divisor of degree 2.
- Open Access
Moduli space of irregular rank two parabolic bundles over the Riemann sphere and its compactification
In this paper, we study rank 2 (quasi) parabolic bundles over the Riemann sphere with an effective divisor and these moduli spaces. First we consider a criterium when a parabolic bundle admits a unramified irregular singular parabolic connection. Second, to give a good compactification of the moduli space of semistable parabolic bundles, we introduce a generalization of parabolic bundles, which is called refined parabolic bundles. Third, we discuss a stability condition of refined parabolic bundles and define elementary transformations of the refined parabolic bundles. Finally, we describe the moduli spaces of refined parabolic bundles when the dimensions of the moduli spaces are two. These are related to geometry of some weak del Pezzo surfaces.
Open AccessModuli space of irregular rank two parabolic bundles over the Riemann sphere and its compactification
In this paper, we study rank 2 (quasi) parabolic bundles over the Riemann sphere with an effective divisor and these moduli spaces. First we consider a criterium when a parabolic bundle admits a unramified irregular singular parabolic connection. Second, to give a good compactification of the moduli space of semistable parabolic bundles, we introduce a generalization of parabolic bundles, which is called refined parabolic bundles. Third, we discuss a stability condition of refined parabolic bundles and define elementary transformations of the refined parabolic bundles. Finally, we describe the moduli spaces of refined parabolic bundles when the dimensions of the moduli spaces are two. These are related to geometry of some weak del Pezzo surfaces.