Related papers: Semisimple Quantum Cohomology and Blow-ups
Global intersection theories for smooth algebraic varieties via products in {\it appropriate}\, Poincar\'e duality theories are obtained. We assume given a (twisted) cohomology theory $H^*$ having a cup product structure and we let consider…
Given a variety $X$ over a perfect field, we study the partition defined on $X$ by the multiplicity (into equimultiple points), and the effect of blowing up at smooth equimultiple centers. Over fields of characteristic zero we prove…
In the first section of this note we show that the Theorem 1.8.1 of Bayer--Manin ([BaMa]) can be strengthened in the following way: {\it if the even quantum cohomology of a projective algebraic manifold $V$ is generically semi--simple, then…
We propose another proof of the geometric class field theory for curves by considering blow-ups of symmetric products of curves.
We prove that under certain conditions, the quantum cohomology of a positively monotone compact symplectic manifold is a deformation of the symplectic cohomology of the complement of a simple crossings symplectic divisor. We also prove…
By utilizing elementary techniques from toric geometry, we prove sharp cohomological vanishing results for line bundles defined on the blow-up of projective space $\mathbb{P}^n$ at no more than $n+1$ points.
Van den Bergh has defined the blowup of a noncommutative surface at a point lying on a commutative divisor. We study one aspect of the construction, with an eventual aim of defining more general kinds of noncommutative blowups. Our basic…
In this paper we prove that cyclic homology, topological cyclic homology, and algebraic $K$-theory satisfy a pro Mayer--Vietoris property with respect to abstract blow-up squares of varieties, in both zero and finite characteristic. This…
Let M be the blow--up of a manifold M along a submanifold X. In this paper we present closed formulae for the integral cohomology and the total Chern class of M. As applications we compute the cohomology of the varieties of complete conics…
We use a sheaf-theoretic approach to obtain a blow-up formula for Dolbeault cohomology groups with values in the holomorphic vector bundle over a compact complex manifold. As applications, we present several positive (or negative) examples…
In the first part of the paper, we give an explicit algorithm to compute the (genus zero) Gromov-Witten invariants of blow-ups of an arbitrary convex projective variety in some points if one knows the Gromov-Witten invariants of the…
The notion of a pseudocycle is introduced by McDuff and Salamon (J-holomorphic curves and quantum cohomology, University Lecture Series, Vol. 6, AMS (1994)) to provide a framework for defining Gromov-Witten invariants and quantum…
We prove that under semismall smooth flops, smooth projective varieties have (non-canonically) isomorphic Chow motives with coefficients in any noetherian local ring $\Lambda$ by comparing the pushforward of the constant intersection…
We study blow-ups in generalized complex geometry. To that end we introduce the concept of holomorphic ideal, which allows one to define a blow-up in the category of smooth manifolds. We then investigate which generalized complex…
We establish blow-up profiles for any blowing-up sequence of solutions of general conformally invariant fully nonlinear elliptic equations on Euclidean domains. We prove that (i) the distance between blow-up points is bounded from below by…
The blow-up for semilinear wave equations with the scale invariant damping has been well-studied for sub-Fujita exponent. However, for super-Fujita exponent, there is only one blow-up result which is obtained in 2014 by Wakasugi in the case…
We obtain non-vanishing of group $L^p$-cohomology of Lie groups for $p$ large and when the degree is equal to the rank of the group. This applies both to semisimple and to some suitable solvable groups. In particular, it confirms that…
A counterexample to the Jordan-H\"older property for semiorthogonal decompositions of derived categories of smooth projective varieties was constructed by B\"ohning, Graf von Bothmer and Sosna. In this short note we present a simpler…
We classify the smooth projective symmetric G-varieties with Picard number one (and G semisimple). Moreover we prove a criterion for the smoothness of the simple (normal) symmetric varieties whose closed orbit is complete. In particular we…
We prove that the quantum cohomology ring of any minuscule or cominuscule homogeneous space, specialized at q=1, is semisimple. This implies that complex conjugation defines an algebra automorphism of the quantum cohomology ring localized…