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European Mathematical Society Publishing House
2024-03-28 17:36:08
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https://www.ems-ph.org/meta/jmeta-stream.php?jrn=PRIMS&vol=52&iss=1&update_since=2024-03-28
Publications of the Research Institute for Mathematical Sciences
Publ. Res. Inst. Math. Sci.
PRIMS
0034-5318
1663-4926
General
10.4171/PRIMS
http://www.ems-ph.org/doi/10.4171/PRIMS
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European Mathematical Society Publishing House
Zuerich, Switzerland
© Research Institute for Mathematical Sciences, Kyoto University
52
2016
1
Nahm's Equations, Quiver Varieties and Parabolic Sheaves
Yuuya
Takayama
Kyoto University, KYOTO, JAPAN
Nahm's equations, handsaw quiver variety, chainsaw quiver variety, parabolic sheaf, instanton, caloron, monopole
We construct an isomorphism between moduli spaces of solutions of Nahm's equations over the circle and framed moduli spaces of locally free parabolic sheaves over $\mathbb P^1 \times \mathbb P^1$ through chainsaw quiver varieties.
Mechanics of particles and systems
Algebraic geometry
1
41
10.4171/PRIMS/172
http://www.ems-ph.org/doi/10.4171/PRIMS/172
Mixed Frobenius Structure and Local Quantum Cohomology
Yukiko
Konishi
Kyoto University, KYOTO, JAPAN
Satoshi
Minabe
Tokyo Denki University, TOKYO, JAPAN
Mixed Frobenius structure, quantum cohomology, local mirror symmetry
In a previous paper, the authors introduced the notion of mixed Frobenius structure (MFS) as a generalization of the structure of a Frobenius manifold. Roughly speaking, the MFS is de fined by replacing a metric of the Frobenius manifold with a fi ltration on the tangent bundle equipped with metrics on its graded quotients. The purpose of the current paper is to construct a MFS on the cohomology of a smooth projective variety whose multiplication is the nonequivariant limit of the quantum product twisted by a concave vector bundle. We show that such a MFS is naturally obtained as the nonequivariant limit of the Frobenius structure in the equivariant setting.
Differential geometry
Algebraic geometry
43
62
10.4171/PRIMS/173
http://www.ems-ph.org/doi/10.4171/PRIMS/173
Basepoint-free Theorem of Reid–Fukuda Type for Quasi-log Schemes
Osamu
Fujino
Kyoto University, KYOTO, JAPAN
Quasi-log schemes, basepoint-free theorem, minimal model program
We introduce various new operations for quasi-log structures. Then we prove a basepoint-free theorem of Reid–Fukuda type for quasi-log schemes as an application.
Algebraic geometry
63
81
10.4171/PRIMS/174
http://www.ems-ph.org/doi/10.4171/PRIMS/174
Microlocal Lefschetz Classes of Graph Trace Kernels
Yuichi
Ike
University of Tokyo, TOKYO, JAPAN
Lefschetz fixed point formulas, microlocal sheaf theory
In this paper, we de fine the notion of graph trace kernels as a generalization of trace kernels. We associate a microlocal Lefschetz class with a graph trace kernel and prove that this class is functorial with respect to the composition of kernels. We apply graph trace kernels to the microlocal Lefschetz fixed point formula for constructible sheaves.
Several complex variables and analytic spaces
Ordinary differential equations
Dynamical systems and ergodic theory
83
101
10.4171/PRIMS/175
http://www.ems-ph.org/doi/10.4171/PRIMS/175