Results 31 to 40 of about 1,900,626 (355)
Explicit equations of the Cartwright-Steger surface [PDF]
Épijournal de Géométrie Algébrique, 2020 We construct explicit equations of Cartwright-Steger and related surfaces.
Lev A. Borisov, Sai-Kee Yeung
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The Loss Surface of Deep Linear Networks Viewed Through the Algebraic Geometry Lens [PDF]
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2018 By using the viewpoint of modern computational algebraic geometry, we explore properties of the optimization landscapes of deep linear neural network models.
D. Mehta +3 more
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Formalization and Implementation of Algebraic Methods in Geometry [PDF]
Electronic Proceedings in Theoretical Computer Science, 2012 We describe our ongoing project of formalization of algebraic methods for geometry theorem proving (Wu's method and the Groebner bases method), their implementation and integration in educational tools.
Filip Marić +3 more
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Hyperelliptic classes are rigid and extremal in genus two [PDF]
Épijournal de Géométrie Algébrique, 2020 We show that the class of the locus of hyperelliptic curves with $\ell$ marked Weierstrass points, $m$ marked conjugate pairs of points, and $n$ free marked points is rigid and extremal in the cone of effective codimension-($\ell + m$) classes on ...
Vance Blankers
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Factorization of the Abel-Jacobi maps [PDF]
Épijournal de Géométrie Algébrique, 2021 As an application of the theory of Lawson homology and morphic cohomology, Walker proved that the Abel-Jacobi map factors through another regular homomorphism. In this note, we give a direct proof of the theorem.
Fumiaki Suzuki
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The construction problem for Hodge numbers modulo an integer in positive characteristic
Forum of Mathematics, Sigma, 2020 Let k be an algebraically closed field of positive characteristic. For any integer $m\ge 2$ , we show that the Hodge numbers of a smooth projective k-variety can take on any combination of values modulo m, subject only to Serre duality.
Remy van Dobben de Bruyn +1 more
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Opers of higher types, Quot-schemes and Frobenius instability loci [PDF]
Épijournal de Géométrie Algébrique, 2020 In this paper we continue our study of the Frobenius instability locus in the coarse moduli space of semi-stable vector bundles of rank $r$ and degree $0$ over a smooth projective curve defined over an algebraically closed field of characteristic $p>0 ...
Kirti Joshi, Christian Pauly
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Algebraic singularities of scattering amplitudes from tropical geometry [PDF]
Journal of High Energy Physics, 2019 We address the appearance of algebraic singularities in the symbol alphabet of scattering amplitudes in the context of planar N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage ...
James R. Drummond +3 more
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Complementary Dual Algebraic Geometry Codes [PDF]
IEEE Transactions on Information Theory, 2016 Linear complementary dual (LCD) codes are a class of linear codes introduced by Massey in 1964. LCD codes have been extensively studied in literature recently.
Sihem Mesnager +2 more
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Hilbert-Mumford stability on algebraic stacks and applications to $\mathcal{G}$-bundles on curves [PDF]
Épijournal de Géométrie Algébrique, 2018 In these notes we reformulate the classical Hilbert-Mumford criterion for GIT stability in terms of algebraic stacks, this was independently done by Halpern-Leinster.
Jochen Heinloth
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