17 citations · 60 across the 9 of their papers we have counts for
10 papers · 1 filter
The web of reflexive polygons is connected
Makoto Miura
We discuss the problem on the connectedness of various webs of lattice polytopes by introducing a geometric point of view from the toric Mori theory. To this end, we provide a comb…
Complete intersection Calabi--Yau threefolds in Hibi toric varieties and their smoothing
Makoto Miura
In this article, we summarize combinatorial description of complete intersection Calabi-Yau threefolds in Hibi toric varieties. Such Calabi-Yau threefolds have at worst conifold si…
Projective reconstruction in algebraic vision
Atsushi Ito, Makoto Miura, Kazushi Ueda
We discuss the geometry of rational maps from a projective space of an arbitrary dimension to the product of projective spaces of lower dimensions induced by linear projections. In…
Derived equivalence and Grothendieck ring of varieties: the case of K3 surfaces of degree 12 and abelian varieties
Atsushi Ito, Makoto Miura, Shinnosuke Okawa +1
In this paper, we discuss the problem of whether the difference of the classes of a Fourier--Mukai pair of smooth projective varieties in the Grothendieck ring o…
-functions of Calabi--Yau 3-folds in Grassmannians
Daisuke Inoue, Atsushi Ito, Makoto Miura
We study -functions of Calabi--Yau 3-folds with Picard number one which are zero loci of general sections of direct sums of globally generated irreducible homogeneous vector bun…
Complete intersection Calabi--Yau manifolds with respect to homogeneous vector bundles on Grassmannians
Daisuke Inoue, Atsushi Ito, Makoto Miura
Based on the method by [Küc95], we give a procedure to list up all complete intersection Calabi--Yau manifolds with respect to direct sums of irreducible homogeneous vector bundles…
The class of the affine line is a zero divisor in the Grothendieck ring: via -Grassmannians
Atsushi Ito, Makoto Miura, Shinnosuke Okawa +1
Motivated by [Bor] and [Mar], we show the equality in the Grothendieck ring of varieties, where is a pair of Calabi-Yau 3…
Calabi--Yau complete intersections in exceptional Grassmannians
Atsushi Ito, Makoto Miura, Shinnosuke Okawa +1
We classify completely reducible equivariant vector bundles on Grassmannians of exceptional Lie groups which give Calabi--Yau 3-folds as complete intersections. In particular, we f…
Seshadri constants and degrees of defining polynomials
Atsushi Ito, Makoto Miura
In this paper, we study a relation between Seshadri constants and degrees of defining polynomials. In particular, we compute the Seshadri constants on Fano varieties obtained as co…
Minuscule Schubert Varieties and Mirror Symmetry
Makoto Miura
We consider smooth complete intersection Calabi-Yau 3-folds in minuscule Schubert varieties, and study their mirror symmetry by degenerating the ambient Schubert varieties to Hibi…