BCOV ring and holomorphic anomaly equation (2008)
We study certain differential rings over the moduli space of Calabi-Yau manifolds. In the case of an elliptic curve, we observe a close relation to the differential ring of quasi-modular forms due to...
Hosono, Shinobu, Konishi, Yukiko
We solve Bershadsky-Cecotti-Ooguri-Vafa (BCOV) holomorphic anomaly equation to determine the higher genus Gromov-Witten invariants ($g \leq 5$) of the derived equivalent Calabi-Yau threefolds, which...
On Stokes Matrices of Calabi-Yau hypersurfaces (2006)
Doran, Charles F., Hosono, Shinobu
We consider Laplace transforms of the Picard-Fuchs differential equations of Calabi-Yau hypersurfaces and calculate their Stokes matrices. We also introduce two different types of Laplace transforms...
Central charges, symplectic forms, and hypergeometric series in local mirror symmetry (2004)
We study a cohomology-valued hypergeometric series which naturally arises in the description of (local) mirror symmetry. We identify it as a central charge formula for BPS states and study its...
Kummer structures on a K3 surface: An old question of T. Shioda (2003)
Hosono, Shinobu, Lian, Bong H., Oguiso, Keiji, Yau, Shing-Tung
We apply our earlier results on Fourier-Mukai partners to answer definitively a question about Kummer surface structures posed by T. Shioda twenty-five years ago.
Counting Unimodular Lattices in $\R^{r,s}$ (2003)
Hosono, Shinobu, Lian, Bong H., Oguiso, Keiji, Yau, Shing-Tung
Narain lattices are unimodular lattices {\it in} $\R^{r,s}$, subject to certain natural equivalence relation and rationality condition. The problem of describing and counting these rational...
c=2 Rational Toroidal Conformal Field Theories via the Gauss Product (2002)
Hosono, Shinobu, Lian, Bong H., Oguiso, Keiji, Yau, Shing-Tung
We find a concise relation between the moduli $\tau, \rho$ of a rational Narain lattice $\Gamma(\tau,\rho)$ and the corresponding momentum lattices of left and right chiral algebras via the Gauss...
Fourier-Mukai partners of a K3 surface of Picard number one (2002)
Hosono, Shinobu, Lian, Bong H., Oguiso, Keiji, Yau, Shing-Tung
We shall give a complete geometrical description of the FM partners of a K3 surface of Picard number 1 and its applications.
Counting BPS States via Holomorphic Anomaly Equations (2002)
We study Gromov-Witten invariants of a rational elliptic surface using holomorphic anomaly equation in [HST1](hep-th/9901151). Formulating invariance under the affine $E_8$ Weyl group symmetry, we...
Kummer structures on a K3 surface - An old question of T. Shioda (2002)
Hosono, Shinobu, Lian, Bong H., Oguiso, Keiji, Yau, Shing-Tung
We apply our earlier results on Fourier-Mukai partners to answer definitively a question about Kummer surface structures, posed by T. Shioda 25 years ago.
Fourier-Mukai number of a K3 surface (2002)
Hosono, Shinobu, Lian, Bong H., Oguiso, Keiji, Yau, Shing-Tung
We shall give a Counting Formula for the number of Fourier-Mukai partners of a K3 surface and consider three applications.
Autoequivalences of Derived Category of A K3 Surface and Monodromy Transformations (2002)
Hosono, Shinobu, Lian, Bong H., Oguiso, Keiji, Yau, Shing-Tung
We consider autoequivalences of the bounded derived category of coherent sheaves on a K3 surface. We prove that the image of the autoequivalences has index at most two in the group of the Hodge...
Relative Lefschetz Action and BPS State Counting (2001)
Hosono, Shinobu, Saito, Masa-Hiko, Takahashi, Atsushi
In this paper, we propose a mathematical definition of a new ``numerical invariants" of Calabi--Yau 3-folds from stable sheaves of dimension one, which is motivated by the Gopakumar-Vafa conjecture...
Relative Lefschetz action and BPS state counting (2001)
Hosono, Shinobu, Saito, Masa-Hiko, Takahashi, Atsushi
In this paper, we propose a mathematical definition of a new “numerical invariants” of Calabi–Yau 3-folds from stable sheaves of dimension one,which is motivated by the Gopakumar-Vafa...
On Mirror Symmetry Conjecture for Schoen's Calabi-Yau 3 folds (1997)
Hosono, Shinobu, Saito, Masa-Hiko, Stienstra, Jan
In this paper, we verify a part of the Mirror Symmetry Conjecture for Schoen's Calabi-Yau 3-fold, which is a special complete intersection in a toric variety. We calculate a part of the prepotential...