Results 11 to 20 of about 11,355 (303)
ORBIT PARAMETRIZATIONS FOR K3 SURFACES [PDF]
Forum of Mathematics, Sigma, 2016 We study moduli spaces of lattice-polarized K3 surfaces in terms of orbits of representations of algebraic groups. In particular, over an algebraically closed field of characteristic 0, we show that in many cases, the nondegenerate orbits of a ...
MANJUL BHARGAVA, WEI HO, ABHINAV KUMAR
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K3 polytopes and their quartic surfaces [PDF]
Advances in Geometry, 2021 AbstractK3 polytopes appear in complements of tropical quartic surfaces. They are dual to regular unimodular central triangulations of reflexive polytopes in the fourth dilation of the standard tetrahedron. Exploring these combinatorial objects, we classify K3 polytopes with up to 30 vertices. Their number is 36 297 333.
Baletti, G., Panizzut, M., Sturmfels, B.
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AN ISOGENY OF K3 SURFACES [PDF]
Bulletin of the London Mathematical Society, 2006 In a recent paper Ahlgren, Ono and Penniston described the L-series of K3 surfaces from a certain one parameter family in terms of those of a particular family of elliptic curves. The Tate conjecture predicts the existence of a correspondence between these K3 surfaces and certain Kummer surfaces related to these elliptic curves.
Bert van Geemen, Jaap Top
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Supersingular K3 surfaces are unirational [PDF]
Inventiones mathematicae, 2014 due to a mistake in Proposition 3.5, the unirationality of supersingular K3 surfaces remains a conjecture: see the appendix for ...
Liedtke, Christian
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Hyperkähler isometries of K3 surfaces [PDF]
Journal of High Energy Physics, 2020 We consider symmetries of K3 manifolds. Holomorphic symplectic automorphisms of K3 surfaces have been classified, and observed to be subgroups of the Mathieu group M 23.
Anindya Banerjee, Gregory W. Moore
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Duke Mathematical Journal, 2022 We complete the remaining cases of the conjecture predicting existence of infinitely many rational curves on K3 surfaces in characteristic zero, prove almost all cases in positive characteristic and improve the proofs of the previously known cases.
Chen, Xi +2 more
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Nagoya Mathematical Journal, 2022 AbstractWe study triple covers of K3 surfaces, following Miranda (1985, American Journal of Mathematics 107, 1123–1158). We relate the geometry of the covering surfaces with the properties of both the branch locus and the Tschirnhausen vector bundle. In particular, we classify Galois triple covers computing numerical invariants of the covering surface ...
ALICE GARBAGNATI, MATTEO PENEGINI
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A Database of Polarized K3 Surfaces [PDF]
Experimental Mathematics, 2007 We describe a computer-based database of polarized K3 surfaces and explain the meaning of the information it contains. In a precise sense, the database includes all K3 surfaces.
Brown, Gavin D., Gavin Brown
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Nikulin involutions on K3 surfaces [PDF]
Mathematische Zeitschrift, 2006 We study the maps induced on cohomology by a Nikulin (i.e. a symplectic) involution on a K3 surface. We parametrize the eleven dimensional irreducible components of the moduli space of algebraic K3 surfaces with a Nikulin involution and we give examples of the general K3 surface in various components.
B. van Geemen, A. Sarti
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Research in Number Theory, 2016 We revisit the mathematics that Ramanujan developed in connection with the famous "taxi-cab" number $1729$. A study of his writings reveals that he had been studying Euler's diophantine equation $$ a^3+b^3=c^3+d^3. $$ It turns out that Ramanujan's work anticipated deep structures and phenomena which have become fundamental objects in arithmetic ...
Ono, Ken, Trebat-Leder, Sarah
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