相关论文: Integral affine structures on spheres III: complet…
Motivated by Calabi's calculation of the second variation sign for locally strongly convex affine maximal surfaces in equiaffine geometry, we first prove that every Calabi extremal surface is also maximal in the Calabi affine geometry. By…
In this paper, we study affine commutative algebraic monoid structures on affine spaces over an arbitrary field of characteristic zero. We obtain full classification of such structures on $\mathbb{A}_K^2$ and $\mathbb{A}_K^3$ and describe…
We study the geometry of M5-branes wrapping a 2-cycle which is Special Lagrangian with respect to a specific complex structure in a Calabi-Yau two-fold. Using methods recently applied to the three-fold case, we are again able find a…
We classify all regular three-dimensional convex cones which possess an automorphism group of dimension at least two, and provide analytic expressions for the complete hyperbolic affine spheres which are asymptotic to the boundaries of…
On one hand, for a general Calabi-Yau complete intersection X, we establish a decomposition, up to rational equivalence, of the small diagonal in X^3, from which we deduce that any decomposable 0-cycle of degree 0 is in fact rationally…
This is the third of a series of papers relating intersections of special cycles on the integral model of a Shimura surface to Fourier coefficients of Hilbert modular forms. More precisely, we embed the Shimura curve over Q associated to a…
This work deals with the study of embeddings of toric Calabi-Yau fourfolds which are complex cones over the smooth Fano threefolds. In particular, we focus on finding various embeddings of Fano threefolds inside other Fano threefolds and…
We consider a generalization of Calabi-Yau structures in the context of $\alpha$-Sasakian manifolds. We study deformations of a special class of Legendrian submanifolds and classify invariant contact Calabi-Yau structures on 5-dimensional…
We describe the intersection complex of any perversity of a toric variety completely in terms of the associated fan. It is described by a finite complex of finite dimensional graded vector spaces which we call graded exterior modules. The…
We study the lattices of algebraic and transcendental cycles of cubic fourfolds.
We study the integral Brauer--Manin obstruction for affine diagonal cubic surfaces, which we employ to construct the first counterexamples to the integral Hasse principle in this setting. We then count in three natural ways how such…
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 of Gel'fand-Kapranov-Zelevinski…
We study the complete intersection property and the algebraic invariants (index of regularity, degree) of vanishing ideals on degenerate tori over finite fields. We establish a correspondence between vanishing ideals and toric ideals…
Continuing from part (I), we develop properties of real intersection theory that turns out to be an extension of the well-established theory in algebraic geometry.
The most impressively prolific exploration of superstring models (aiming for our physical reality) has been focused on worldsheet-supersymmetric gauged linear sigma models and the closely associated complex-algebraic toric geometry. Mirror…
This is a short introduction to the study of compactifications of F-theory on elliptic Calabi-Yau threefolds near colliding singularities. In particular we consider the case of non-transversal intersections of the singular fibers.
We derive a formula for the Milnor class of scheme-theoretic global complete intersections (with arbitrary singularities) in a smooth variety in terms of the Segre class of its singular scheme. In codimension one the formula recovers a…
In this paper, the numbers of rational curves on general complete intersection Calabi-Yau threefolds in complex projective spaces are computed up to degree six. The results are all in agreement with the predictions made from mirror…
The general quintic hypersurface in ${\mathbb P}^4$ is the most famous example of a Calabi--Yau threefold for which mirror symmetry has been investigated in detail. There is a description of the mirror as a hypersurface in a certain…
Matrix factorizations of a hypersurface yield a description of the asymptotic structure of minimal free resolutions over the hypersurface. We introduce a new concept of matrix factorizations for complete intersections that allows us to…