Related papers: Algebraic surfaces and Seiberg-Witten invariants
In the previous article, we showed the Rasmussen-Tamagawa conjecture for QM-abelian surfaces over imaginary quadratic fields. In this article, we generalize the previous work to QM-abelian surfaces over number fields of higher degree. We…
We present an overview of the differential geometry of curves and surfaces using examples from soft matter as illustrations. The presentation requires a background only in vector calculus and is otherwise self-contained.
This is an English translation of the expository article written by the author in Japanese for publication in {\em Sugaku}. The author will explain Milnor invariants from the viewpoint of his research.
We corrected a few errors in the previous submission. These do not affect any of the topological conclusions of the earlier version. We have also included a few observations about the Casson invariant of the Brieskorn homology spheres.
In this short paper we compute the values of Dijkgraaf-Witten invariants over $Z_2$ for all orientable Seifert manifolds with orientable bases.
This is an extended abstract of my talk at the Oberwolfach Workshop "Representation Theory of Quivers and Finite-Dimensional Algebras" (February 12 - February 18, 2023 ). It is based on a joint work with R. Bennett-Tennenhaus…
We calculate the Seiberg-Witten invariants of branched covers of prime degree, where the branch locus consists of embedded spheres. Aside from the formula itself, our calculations give rise to some new constraints on configurations of…
We present a covariant formulation of the Gauss-Weingarten equations and the Gauss-Mainardi-Codazzi equations for surfaces in 3-dimensional curved spaces. We derive a coordinate invariant condition on the first and second fundamental form…
This is a survey paper on Alegbraic Geometry over Lie Algebras
We propose an abelian categorification of $\hat{Z}$-invariants for Seifert $3$-manifolds. First, we give a recursive combinatorial derivation of these $\hat{Z}$-invariants using graphs with certain hypercubic structures. Next, we consider…
The modified Seiberg-Witten monopole equations are presented in this letter. These equations have analytic solutions in the whole 1+3 Minkowski space with finite energy. The physical meaning of the equations and solutions are discussed…
We show that the algebraic and the symplectic GW-inivariants of smooth projective varieties are equivalent.
A formula is given for the Seiberg-Witten invariants of a 4-manifold that is cut along certain kinds of 3-dimensional tori. The formula involves a Seiberg-Witten invariant for each of the resulting pieces.
By analytic deformations of complex structures, we mean perturbations of the Dolbeault operator. By algebraic deformations of complex structures, we mean deformations of holomorphic glueing data. For complex manifolds there is,…
Minor changes in the exposition and small corrections on the previous version.
For any smooth complex projective surface $S$, we construct semistable refined Vafa-Witten invariants of $S$ which prove the main conjecture of arXiv:1810.00078. This is done by extending part of Joyce's universal wall-crossing formalism to…
This is an overview of my papers arxiv:1602.04254 and arxiv:1604.01588.
Rejoinder of "Instrumental Variables: An Econometrician's Perspective" by Guido W. Imbens [arXiv:1410.0163].
We study involutions on K3 surfaces under conjugation by derived equivalence and more general relations, together with applications to equivariant birational geometry.
Let $S_g$ ($g\geq 2$) be a closed surface of genus $g$. Let $K$ be any real number field and $A$ be any quaternion algebra over $K$ such that $A\otimes_K\mathbb{R}\cong M_2(\mathbb{R})$. We show that there exists a hyperbolic structure on…