Related papers: An operadic proof of the BTT Theorem
We prove derived equivalence of Calabi-Yau threefolds constructed by Ito-Miura-Okawa-Ueda as an example of non-birational Calabi-Yau varieties whose difference in the Grothendieck ring of varieties is annihilated by the affine line.
Built upon the proposal of Kaplan et.al. [hep-lat/0206109], we construct noncommutative lattice gauge theory with manifest supersymmetry. We show that such theory is naturally implementable via orbifold conditions generalizing those used by…
Let $X$ be a normal projective variety admitting a polarized endomorphism $f$, i.e., $f^*H\sim qH$ for some ample divisor $H$ and integer $q>1$. Then Broustet and Gongyo proposed the conjecture that $X$ is of Calabi-Yau type (CY for short),…
We prove a general criterion for a von Neumann algebra $M$ in order to be in standard form. It is formulated in terms of an everywhere defined, invertible, antilinear, a priori not necessarily bounded operator, intertwining $M$ with its…
Given a differential operator of geometric origin there exists a list of operations that preserve this property, e.g., tensor products, pull-backs, push-forwards and the middle convolution. We apply certain sequences of these operations to…
We study neutral functional differential equations with stable linear non-autonomous $D$-operator. The operator of convolution $\hat{D}$ transforms $BU$ into $BU$. We show that, if $D$ is stable, then $\hat{D}$ is invertible and, besides,…
We provide the first explicit example of Type IIB string theory compactification on a globally defined Calabi-Yau threefold with torsion which results in a four-dimensional effective theory with a non-Abelian discrete gauge symmetry. Our…
We prove a generic Torelli theorem for a class of three-dimensional log Calabi--Yau pairs $(Y, D)$ with maximal boundary.
A few years ago, Fang, Lu and Yoshikawa conjectured that a certain string-theoretic invariant of Calabi-Yau threefolds is a birational invariant. We prove a weak form of this conjecture.
We prove a version of the Fatou theorem for bounded functions with bounded d_J-bar diferential on wedge-type domains in an almost complex manifold.
We show how F-theory on a Calabi-Yau (n+1)-fold, in appropriate limit, can be identified as an orientifold of type IIB string theory compactified on a Calabi-Yau n-fold.
We expand the theory of log canonical $3$-fold complements. We prove that if $X\rightarrow T$ is a $3$-dimensional contraction of log Calabi-Yau type, then we can find $B\geq 0$ on $X$ for which $(X,B)$ is log canonical and $n(K_X+B)\sim_T…
We show that an algebraic 2-Calabi-Yau triangulated category over an algebraically closed field is a cluster category if it contains a cluster tilting subcategory whose quiver has no oriented cycles. We prove a similar characterization for…
We establish a global Torelli theorem for the complete family of Calabi-Yau threefolds arising from cyclic triple covers of $\mathbb P^3$ branched along stable hyperplane arrangements.
We consider the conversion problem for multimodal type theory (MTT) by characterizing the normal forms of the type theory and proving normalization. Normalization follows from a novel adaptation of Sterling's Synthetic Tait Computability…
We prove that the open topological string partition function on a D-brane configuration in a Calabi-Yau manifold X takes the form of a closed topological string partition function on a different Calabi-Yau manifold X_b. This identification…
Modular invariance is a necessary condition for the consistency of any closed string theory. In particular, it imposes stringent constraints on the spectrum of orbifold theories, and in principle determines their spectrum uniquely up to…
We prove Fatou's theorem for nonnegative harmonic functions with respect to subordinate Brownian motions with Gaussian components on bounded $C^{1,1}$ open sets $D$. We prove that nonnegative harmonic functions with respect to such…
Let $Y$ be an abelian variety over a subfield $k \subset \mathbb{C}$ that is of finite type over $\mathbb{Q}$. We prove that if the Mumford-Tate conjecture for $Y$ is true, then also some refined integral and adelic conjectures due to Serre…
Bershadsky, Cecotti, Ooguri, and Vafa constructed a real-valued invariant for Calabi--Yau manifolds, which is now called the BCOV torsion. Based on it, a metric-independent invariant, called the BCOV invariant, was constructed by…