Related papers: Varieties with two smooth blow up structures

This note is devoted to a special Fano fourfold defined by a four-dimensional space of skew-symmetric forms in five variables. This fourfold appears to be closely related with the classical Segre cubic and its Cremona-Richmond configuration…

Here we consider the product of varieties with $n$-blocks collections . We give some cohomological splitting conditions for rank 2 bundles. A cohomological characterization for vector bundles is also provided. The tools are Beilinson's type…

In 2001, de Oliveira, Katzarkov, and Ramachandran conjectured that the property of smooth projective varieties having big fundamental groups is stable under small deformations. This conjecture was proven by Beno\^it Claudon in 2010 for…

The Hilbert scheme $X^{[3]}$ of length-$3$ subschemes of a smooth projective variety $X$ is known to be smooth and projective. We investigate whether the property of having a multiplicative Chow-Kuenneth decomposition is stable under taking…

The harmonic map heat flow is a geometric flow well known to produce solutions whose gradient blows up in finite time. A popular model for investigating the blow-up is the heat flow for maps $\mathbb R^{d}\to S^{d}$, restricted to…

Let E be a rank two vector bundle on a scheme X. The following three structures are shown to be equivalent : a) A primitive quadratic map q: E --> L, with values in an invertible module L. b) A double covering f: Y --> X endowed with an…

Algebraic varieties which are locally isomorphic to open subsets of affine space will be called {\em plain}. Plain varieties are smooth and rational. The converse is true for curves and surfaces, and unknown in general. It is shown that…

A smooth scheme X over a field k of positive characteristic is said to be strongly liftable, if X and all prime divisors on X can be lifted simultaneously over W_2(k). In this paper, first we prove that smooth toric varieties are strongly…

We classify smooth toric Fano varieties of dimension $n\geq 3$ containing a toric divisor isomorphic to $\PP^{n-1}$. As a consequence of this classification, we show that any smooth complete toric variety $X$ of dimension $n\geq 3$ with a…

We prove several statements about arithmetic hyperbolicity of certain blow-up varieties. As a corollary we obtain multiple examples of simply connected quasi-projective varieties that are pseudo-arithmetically hyperbolic. This generalizes…

We prove a decomposition theorem of the quantum cohomology D-module of the blowup of a smooth projective variety X along a smooth subvariety Z. The main tools we use are shift operators and Fourier analysis for equivariant quantum…

Given a sequence of point blow-ups of smooth n-dimensional projective varieties $Z_{i}$ defined over an algebraically closed field k, $Z_{s}\rightarrow Z_{s-1}\rightarrow ...\rightarrow Z_{1}\rightarrow Z_{0}$, we give two presentations of…

Let f: X -> Z be a local, projective, divisorial contraction between normal varieties of dimension n with Q-factorial singularities. Let $Y \subset X$ be a f-ample Cartier divisor and assume that f|Y: Y -> W has a structure of a weighted…

We study monoidal 2-categories and bicategories in terms of categorical extensions and the cohomological data they determine in appropriate cohomology theories with coefficients in Picard groupoids. In particular, we analyze the hierarchy…

We construct a smooth Artin stack parameterizing the stable weighted curves of genus one with twisted fields and prove that it is isomorphic to the blowup stack of the moduli of genus one weighted curves studied by Hu and Li. This leads to…

Going one step further in Zak's classification of Scorza varieties with secant defect equal to one, we characterize the Veronese embedding of $\P^n$ given by the complete linear system of quadrics and its smooth projections from a point as…

We prove that, for a natural class of Bridgeland stability conditions on $\mathbb{P}^1\times\mathbb{P}^1$ and the blow-up of $\mathbb{P}^2$ at a point, the moduli spaces of Bridgeland semistable objects are projective. Our technique is to…

Two birational projective varieties in $P^n$ are Cremona Equivalent if there is a birational modification of $P^n$ mapping one onto the other. The minimal Cremona degree of $X\subset P^n$ is the minimal integer among all degrees of…

Using a filtration on the Grothendieck ring of triangulated categories, we define the categorical dimension of a birational map between smooth projective varieties. We show that birational automorphisms of bounded categorical dimension form…

We study the geometry of a class of $n$-dimensional smooth projective varieties constructed by Schreieder for their noteworthy Hodge-theoretic properties. In particular, we realize Schreieder's surfaces as elliptic modular surfaces and…