相关论文: Exceptional collections on certain Hassett spaces

Continuing the formulation of finite $N$ Hilbert spaces in emergent theories we study in this work $S_{N}$ symmetric collective models. For the case of $N$ bosons in $d$ dimensions, which map to matrix models with commuting matrices, we…

Using cyclotomic specializations of the equivariant $K$-theory with respect to a torus action we derive congruences for discrete invariants of exceptional objects in derived categories of coherent sheaves on a class of varieties that…

We apply the recent results of Galkin et al. [GKMS15] to study some geometrical features of Keum's fake projective planes. Among other things, we show that the bicanonical map of Keum's fake projective planes is always an embedding.…

We characterize transversality, non-transversality properties on the moduli space of genus 0 stable maps to a rational projective surface. If a target space is equipped with a real structure, i.e, anti-holomorphic involution, then the…

The algebras of valuations on $S^6$ and $S^7$ invariant under the actions of $\mathrm G_2$ and $\mathrm{Spin}(7)$ are shown to be isomorphic to the algebra of translation-invariant valuations on the tangent space at a point invariant under…

We show that in a smooth family of complete varieties, the existence of full exceptional collection on a fiber preserves for the fibers in a neighborhood. Then we show that the noncommutative deformations of a strong exceptional collection…

We construct the Einstein equation for an invariant Riemannian metric on the exceptional full flag manifold $M=G_2/T$. By computing a Gr\"obner basis for a system of polynomials of multi-variables we prove that this manifold admits exactly…

In this article we provide a detailed description of a technique to obtain a simple parametrization for different exceptional Lie groups, such as G2, F4 and E6, based on their fibration structure. For the compact case, we construct a…

It is expected that a totally invariant divisor of a non-isomorphic endomorphism of the complex projective space is a union of hyperplanes. In this paper, we compute an upper bound for the degree of such a divisor. As a consequence, we…

The first part of this work constructs positive-genus real Gromov-Witten invariants of real-orientable symplectic manifolds of odd "complex" dimensions; the present part focuses on their properties that are essential for actually working…

In this paper, we prove that any two birational projective varieties with finite quotient singularities can be realized as two geometric GIT quotients of a non-singular projective variety by a reductive algebraic group. Then, by applying…

We construct a Grothendieck-Witt space for any stable infinity category with duality. If we apply our construction to perfect complexes over a commutative ring in which 2 is invertible we recover the classical Grothendieck-Witt space. Our…

For a stability condition $\sigma$ on a triangulated category, Dimitrov-Katzarkov introduced the notion of a $\sigma$-exceptional collection. In this paper, we study full $\sigma$-exceptional collections in the derived category of an…

Let X be an algebraic variety with an action of an algebraic group G. Suppose X has a full exceptional collection of sheaves, and these sheaves are invariant under the action of the group. We construct a semiorthogonal decomposition of…

A collection $\mathcal S$ of equivalence classes of positive definite integral quadratic forms in $n$ variables is called an $n$-exceptional set if there exists a positive definite integral quadratic form which represents all equivalence…

Consider $(\mathbb{C}^*)^k$ acting on $\mathbb{C}^N$ satisfying certain 'quasi-symmetric' condition which produces a class of toric Calabi-Yau GIT quotient stacks. Using subcategories of $Coh([\mathbb{C}^N / (\mathbb{C}^*)^k])$ generated by…

In this work, we are interested in characterizing typical (generic) dimensional properties of invariant measures associated with the full-shift system, $T$, in a product space whose alphabet is a perfect and separable metric space (thus,…

We construct two parametrizations of the non compact exceptional Lie group G=E7(-25), based on a fibration which has the maximal compact subgroup K=(E6 x U(1))/Z_3 as a fiber. It is well known that G plays an important role in the N=2 d=4…

We consider the Whitney problem for valuations: does a smooth $j$-homogeneous translation-invariant valuation on $\mathbb R^n$ exist that has given restrictions to a fixed family $S$ of linear subspaces? A necessary condition is…

This paper gives a complete answer of the following question: which (singular, projective) curves have a categorical resolution of singularities which admits a full exceptional collection? We prove that such full exceptional collection…