Cremona transformations and derived equivalences of K3 surfaces
نویسندگان
چکیده
منابع مشابه
Equivalences of Derived Categories and K3 Surfaces
We consider derived categories of coherent sheaves on smooth projective varieties. We prove that any equivalence between them can be represented by an object on the product. Using this, we give a necessary and sufficient condition for equivalence of derived categories of two K3 surfaces.
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We show that there exist a complex projective K3 surface X and an automorphism σ ∈ Aut(C) such that the conjugate K3 surface X is a non-isomorphic Fourier Mukai partner of X.
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Consider the gradient map associated to any non-constant homogeneous polynomial f ∈ C[x0, . . . , xn] of degree d, defined by φf = grad(f) : D(f) → P , (x0 : . . . : xn) → (f0(x) : . . . : fn(x)) whereD(f) = {x ∈ P; f(x) 6= 0} is the principal open set associated to f and fi = ∂f ∂xi . This map corresponds to polar Cremona transformations. In Proposition 3.4 we give a new lower bound for the de...
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In 1883 Kantor' stated and attempted a demonstration of a theorem which asserted that the satisfaction of a system of equations by a certain set of positive integers was sufficient to assure that these integers would represent a planar Cremona transformation. Since then the theorem has been repeated several times in the literature. Recently Coolidge2 attached new significance to the theorem and...
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We compute the multidegrees and the Segre numbers of general determinantal Cremona transformations, with generically reduced base scheme, by specializing to the standard Cremona transformation and computing its Segre class via mixed volumes of rational polytopes. Dedicated to the memory of Shiing-Shen Chern
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2018
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x18007145