A geometric proof of Kummer's reciprocity law for seventh powers
A Geometric Study of the Monodromy of Complex Analytic Surfaces.
A Geometrical approach to Gordan--Noether's and Franchetta's contributions to a question posed by Hesse.
A geometrical approach to the theory of Jacobi forms
A Geometrical Construction for the Polynomial Invariants of some Reflection Groups
2000 Mathematics Subject Classification: Primary 20F55, 13F20; Secondary 14L30.We construct invariant polynomials for the reflection groups [3, 4, 3] and [3, 3, 5] by using some special sets of lines on the quadric P1 × P1 in P3. Then we give a simple proof of the well known fact that the ring of invariants are rationally generated in degree 2,6,8,12 and 2,12,20,30.
A Geometrie Approach to Keller's Jacobian Conjecture.
A Gersten–Witt spectral sequence for regular schemes
A global mirror symmetry framework for the Landau–Ginzburg/Calabi–Yau correspondence
We show how the Landau–Ginzburg/Calabi–Yau correspondence for the quintic three-fold can be cast into a global mirror symmetry framework. Then we draw inspiration from Berglund–Hübsch mirror duality construction to provide an analogue conjectural picture featuring all Calabi–Yau hypersurfaces within weighted projective spaces and certain quotients by finite abelian group actions.
A Global Moduli Space of Ample Subvarieties on Compact Kähler Manifolds with Very Strongly Negative Curvature.
A graph-theoretic method for choosing a spanning set for a finite-dimensional vector space, with applications to the Grossman-Larson-Wright module and the Jacobian conjecture.
A Grothendieck-Riemann-Roch Formula for Maps of Complex Manifolds.
A group action on Losev-Manin cohomological field theories
We discuss an analog of the Givental group action for the space of solutions of the commutativity equation. There are equivalent formulations in terms of cohomology classes on the Losev-Manin compactifications of genus moduli spaces; in terms of linear algebra in the space of Laurent series; in terms of differential operators acting on Gromov-Witten potentials; and in terms of multi-component KP tau-functions. The last approach is equivalent to the Losev-Polyubin classification that was obtained...
A group law on smooth real quartics having at least real branches
Let be a smooth real quartic curve in . Suppose that has at least real branches . Let and let . Let be the map from into the neutral component Jac of the set of real points of the jacobian of , defined by letting be the divisor class of the divisor . Then, is a bijection. We show that this allows an explicit geometric description of the group law on Jac. It generalizes the classical geometric description of the group law on the neutral component of the set of real points of...
A Hasse principle for two dimensional global fields.
A Hessenberg generalization of the Garsia-Procesi basis for the cohomology ring of Springer varieties.
A higher Albanese map for complex threefolds based on a construction by M. Green
We construct a higher Abel-Jacobi map for 0-cycles on complex threefolds and prove that it can be used to describe Mumford's pull-back of a differential form, and that its image is infinite-dimensional in many cases. However, making a certain assumption, we show that it is not always injective.
A Higher Dimensional Analogue of Mordell's Conjecture Over Function Fields.
A Hilbert-Mumford criterion for SL₂-actions
Let the special linear group G : = SL₂ act regularly on a ℚ-factorial variety X. Consider a maximal torus T ⊂ G and its normalizer N ⊂ G. We prove: If U ⊂ X is a maximal open N-invariant subset admitting a good quotient U → U ⃫N with a divisorial quotient space, then the intersection W(U) of all translates g · U is open in X and admits a good quotient W(U) → W(U) ⃫G with a divisorial quotient space. Conversely, we show that every maximal open G-invariant subset W ⊂ X admitting a good quotient W...
A Hirzebruch-Riemann-Roch formula for analytic spaces and non-projective algebraic varieties
A Hodge type decomposition for spinor valued forms