Related papers: A note on a Griffiths-type ring for complete inter…

Let $C$ be a smooth projective curve of genus $2$. Following a method by O' Grady, we construct a semismall desingularization $\tilde{\mathcal{M}}_{Dol}^G$ of the moduli space $\mathcal{M}_{Dol}^G$ of semistable $G$-Higgs bundles of degree…

For an arbitrary semisimple Frobenius manifold we construct Hodge integrable hierarchy of Hamiltonian partial differential equations. In the particular case of quantum cohomology the tau-function of a solution to the hierarchy generates the…

We study the moduli space of smooth complete intersections of two quadrics in $\mathbb{P}^n$ by relating it to the geometry of the singular members of the corresponding pencils. Giving an alternative presentation for the moduli space of…

We establish a link between the GIT stability of complete intersections of same degree hypersurfaces in the same ambient projective space, which can be parametrised as tuples in a Grassmanian scheme, and the log canonical thresholds of…

For $G = \mathrm{GL}_2, \mathrm{SL}_2, \mathrm{PGL}_2$ we compute the intersection E-polynomials and the intersection Poincar\'e polynomials of the $G$-character variety of a compact Riemann surface $C$ and of the moduli space of $G$-Higgs…

We improve the known Hodge type bound for the exotic cohomology of complete intersections. In the revised version, we included a simplification of our original argument due to Pierre Deligne. The note appears in the C. R. de l'Aca. des Sc.…

A complete treatment of the intersections of two geodesics on the surface of an ellipsoid of revolution is given. With a suitable metric for the distances between intersections, bounds are placed on their spacing. This leads to fast and…

We determine the Hochschild cohomology algebras of the square-free monomial complete intersections. In particular, we provide a formula for the cup product which gives the cohomology module an algebra structure and then we describe this…

A generalization of the formula of Fine and Rao for the ranks of the intersection homology groups of a complex algebraic variety is given. The proof uses geometric properties of intersection homology and mixed Hodge theory.

We prove that any three-point genus zero Gromov-Witten invariant on a type A Grassmannian is equal to a classical intersection number on a two-step flag variety. We also give symplectic and orthogonal analogues of this result; in these…

In this paper we prove a residue formula for intersection pairings of reduced spaces of certain quasi-Hamiltonian G-spaces, by constructing the corresponding Hamiltonian G-space. Our argument closely follows the methods of a 1998 paper of…

In this paper, we define and study Clifford quadratic complete intersections. After showing some properties of Clifford quantum polynomial algebras, we show that there is a natural one-to-one correspondence between Clifford quadratic…

It is proved in this paper that a locally complete intersection curve in a smooth affine C-algebra with trival conormal bundle is a set theoretic complete intersection if its corresponding class in the Grothendieck Group is torsion.

We compute the intersection cohomology of the moduli spaces $M_{r,d}$ of semistable vector bundles having rank $r$ and degree $d$ over a curve. We do this by relating the Hodge-Deligne polynomial of the intersection cohomology of $M_{r,d}$…

We consider the coincidence problem for the square lattice that is translated by an arbitrary vector. General results are obtained about the set of coincidence isometries and the coincidence site lattices of a shifted square lattice by…

For a Riemannian $G$-structure, we compute the divergence of the vector field induced by the intrinsic torsion. Applying the Stokes theorem, we obtain the integral formula on a closed oriented Riemannian manifold, which we interpret in…

We construct an explicit homotopy formula for the d-bar complex on a complete intersection subvariety V in CP^n. This formula can be interpreted as a Hodge-type decomposition for residual currents on V.

We prove an explicit combinatorial formula for the structure constants of the Grothendieck ring of a Grassmann variety with respect to its basis of Schubert structure sheaves. We furthermore relate K-theory of Grassmannians to a bialgebra…

We give a formula for the geometric fixed-points spectrum of the real topological cyclic homology of a bounded below ring spectrum, as an equaliser of two maps between tensor products of modules over the norm. We then use this formula to…

This paper initiates a study of Hodge integrals on moduli spaces of pseudostable curves. We prove an explicit comparison formula that allows one to effectively compute any pseudostable Hodge integral in terms of intersection numbers on…