Related papers: A Proof On Arnold-Chekanov Conjecture

In this article, we give proofs on the Arnold Lagrangian intersection conjecture on the cotangent bundles, Arnold-Givental Lagrangian intersection conjecture and the Arnold fixed point conjecture.

We prove the Arnold chord conjecture on cotangent bundles of open manifold by Gromov's nonlinear Fredholm alternative for $J-$holomorphic curves.

In this note we give a short proof of Arnold's conjecture for the zero section of a cotangent bundle of a closed manifold. The proof is based on some basic properties of Lagrangian spectral invariants from Floer theory.

We prove the Shafarevich conjecture for varieties with globally generated cotangent bundle, subject to mild numerical conditions.

We give an proof on the Weinstein conjecture on the cotangent bundles of open manifolds. Its proof is based on Gromov's nonlinear Fredholm alternative.

We give new proofs on Arnold Chord Conjecture and Weinstein Conjecture in M\times C which generalizes the previous works.

The paper generalizes a result of Behrend-Fantechi and Baranovsky-Ginzburg to the 1-shifted cotangent bundle $T^*X[1]$ of a smooth scheme $X$ over the field of complex numbers. We show how one can obtain twisted cotangent bundles as derived…

In this note, we extend the theories of the canonical bundle formula and adjunction to the case of generalized pairs. As an application, we study a particular case of a conjecture by Prokhorov and Shokurov.

A conic bundle is a contraction $X\to Z$ between normal varieties of relative dimension $1$ such that $-K_X$ is relatively ample. We prove a conjecture of Shokurov which predicts that, if $X\to Z$ is a conic bundle such that $X$ has…

We prove a Chekanov-type theorem for the spherization of the cotangent bundle $ST^*B$ of a closed manifold $B$. It claims that for Legendrian submanifolds in $ST^*B$ the property "to be given by a generating family quadratic at infinity"…

We prove the Conley conjecture for cotangent bundles of oriented, closed manifolds, and Hamiltonians which are quadratic at infinity, i.e., we show that such Hamiltonians have infinitely many periodic orbits. For the conservative systems,…

The gonality conjecture predicts that the gonality of a curve can be read off Koszul cohomology of line bundles of sufficiently large degree. We verify this conjecture for generic curves of odd genus. The even-genus case was previously…

We prove a generalization of Fulton's conjecture which relates intersection theory on an arbitrary flag variety to invariant theory.

This is a summary of the proof of BAB conjecture. All material are taken from the two BAB paper in the reference. The aim of this summary is to help reader to understand the more technical side of the proof of BAB.

In this paper we establish effective lower bounds on the degrees of the Debarre and Kobayashi conjectures. Then we study a more general conjecture proposed by Diverio-Trapani on the ampleness of jet bundles of general complete intersections…

In this short note, we prove a Tamarkin-type separation theorem for possibly non-compact subsets in cotangent bundles.

In this note we investigate the Cheltsov--Rubinstein conjecture. We show that this conjecture does not hold in general and some counterexamples will be presented.

Using compactifications in the logarithmic cotangent bundle, we obtain a formula for the Chern classes of the pushforward of Lagrangian cycles under an open embedding with normal crossing complement. This generalizes earlier results of…

We give counterexamples to Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients.

In this note we observe that Arnold conjecture for the Hamiltonian maps still holds on weighted projective spaces $\CP^n({\bf q})$, and that Arnold conjecture for the Lagrange intersections for $(\CP^n({\bf q}), \RP^n({\bf q}))$ is also…