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Virtual resolutions for a product of projective spaces 投影空间乘积的虚分辨率
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2017-03-22 DOI: 10.14231/ag-2020-013
Christine Berkesch Zamaere, D. Erman, Gregory G. Smith
{"title":"Virtual resolutions for a product of projective spaces","authors":"Christine Berkesch Zamaere, D. Erman, Gregory G. Smith","doi":"10.14231/ag-2020-013","DOIUrl":"https://doi.org/10.14231/ag-2020-013","url":null,"abstract":"Syzygies capture intricate geometric properties of a subvariety in projective space. However, when the ambient space is a product of projective spaces or a more general smooth projective toric variety, minimal free resolutions over the Cox ring are too long and contain many geometrically superfluous summands. In this paper, we construct some much shorter free complexes that better encode the geometry.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2017-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48695814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 39
The tropical superpotential for $mathbb{P}^2$ $mathbb｛P｝^2的热带超势$
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2017-03-22 DOI: 10.14231/ag-2020-002
T. Prince
{"title":"The tropical superpotential for $mathbb{P}^2$","authors":"T. Prince","doi":"10.14231/ag-2020-002","DOIUrl":"https://doi.org/10.14231/ag-2020-002","url":null,"abstract":"We present an extended worked example of the computation of the tropical superpotential considered by Carl--Pumperla--Siebert. In particular we consider an affine manifold associated to the complement of a non-singular genus one plane curve, and calculate the wall and chamber decomposition determined by the Gross--Siebert algorithm. Using the results of Carl--Pumperla--Siebert we determine the tropical superpotential, via broken line counts, in every chamber of this decomposition. The superpotential defines a Laurent polynomial in every chamber, which we demonstrate to be identical to the Laurent polynomials predicted by Coates--Corti--Galkin--Golyshev--Kaspzryk to be mirror to $mathbb{P}^2$.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2017-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43057538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
K�hlerness of moduli spaces of stable sheaves over non-projective K3 surfaces 非射影K3曲面上稳定轮轴模空间的K度
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2017-03-06 DOI: 10.14231/AG-2019-020
A. Perego
{"title":"K�hlerness of moduli spaces of stable sheaves over non-projective K3 surfaces","authors":"A. Perego","doi":"10.14231/AG-2019-020","DOIUrl":"https://doi.org/10.14231/AG-2019-020","url":null,"abstract":"We show that a moduli space of slope-stable sheaves over a K3 surface is an irreducible hyperk\"ahler manifold if and only if its second Betti number is the sum of its Hodge numbers $h^{2,0}$, $h^{1,1}$ and $h^{0,2}$.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2017-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49205594","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
The tautological ring of $mathcal{M}_{g,n}$ via Pandharipande�Pixton�Zvonkine $r$-spin relations 通过Pandharipande ` ` Pixton ` ` Zvonkine $r$-自旋关系的$mathcal{M}_{g,n}$的重言环
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2017-03-02 DOI: 10.14231/AG-2018-019
Reinier Kramer, Farrokh Labib, D. Lewanski, S. Shadrin
{"title":"The tautological ring of $mathcal{M}_{g,n}$ via Pandharipande�Pixton�Zvonkine $r$-spin relations","authors":"Reinier Kramer, Farrokh Labib, D. Lewanski, S. Shadrin","doi":"10.14231/AG-2018-019","DOIUrl":"https://doi.org/10.14231/AG-2018-019","url":null,"abstract":"We use relations in the tautological ring of the moduli spaces Mg,n derived by Pandharipande, Pixton, and Zvonkine from the Givental formula for the r-spin Witten class in order to obtain some restrictions on the dimensions of the tautological rings of the open moduli spacesMg,n. In particular, we give a new proof for the result of Looijenga (for n = 1) and Buryak et al. (for n > 2) that dimRg-1(Mg,n) ≤ n. We also give a new proof of the result of Looijenga (for n = 1) and Ionel (for arbitrary n > 1) that Ri(Mg,n) = 0 for i > g and give some estimates for the dimension of Ri(Mg,n) for i ≤ g - 2.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":"1 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2017-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41775270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
A generic global Torelli theorem for certain Horikawa surfaces 一类Horikawa曲面的一般全局Torelli定理
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2017-02-20 DOI: 10.14231/ag-2019-007
G. Pearlstein, Zhenghe Zhang
{"title":"A generic global Torelli theorem for certain Horikawa surfaces","authors":"G. Pearlstein, Zhenghe Zhang","doi":"10.14231/ag-2019-007","DOIUrl":"https://doi.org/10.14231/ag-2019-007","url":null,"abstract":"Algebraic surfaces of general type with $q=0$, $p_g=2$ and $K^2=1$ were described by Enriques and then studied in more detail by Horikawa. In this paper we consider a $16$-dimensional family of special Horikawa surfaces which are certain bidouble covers of $mathbb{P}^2$. The construction is motivated by that of special Kunev surfaces which are counterexamples for infinitesimal Torelli and generic global Torelli problem. The main result of the paper is a generic global Torelli theorem for special Horikawa surfaces. To prove the theorem, we relate the periods of special Horikawa surfaces to the periods of certain lattice polarized $K3$ surfaces using eigenperiod maps and then apply a Torelli type result proved by Laza.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2017-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43584246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
Open surfaces of small volume 小体积的开放表面
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2016-12-29 DOI: 10.14231/AG-2019-015
V. Alexeev, Wenfei Liu
{"title":"Open surfaces of small volume","authors":"V. Alexeev, Wenfei Liu","doi":"10.14231/AG-2019-015","DOIUrl":"https://doi.org/10.14231/AG-2019-015","url":null,"abstract":"We construct a surface with log terminal singularities and ample canonical class that has $K_X^2=1/48 983$ and a log canonical pair $(X,B)$ with a nonempty reduced divisor $B$ and ample $K_X+B$ that has $(K_X+B)^2 = 1/462$. Both examples significantly improve known records.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":"1 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2016-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66814898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 18
Effective algebraic integration in bounded genus 有界属的有效代数积分
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2016-12-21 DOI: 10.14231/AG-2019-021
J. Pereira, R. Svaldi
{"title":"Effective algebraic integration in bounded genus","authors":"J. Pereira, R. Svaldi","doi":"10.14231/AG-2019-021","DOIUrl":"https://doi.org/10.14231/AG-2019-021","url":null,"abstract":"We introduce and study birational invariants for foliations on projective surfaces built from the adjoint linear series of positive powers of the canonical bundle of the foliation. We apply the results in order to investigate the effective algebraic integration of foliations on the projective plane. In particular, we describe the Zariski closure of the set of foliations on the projective plane of degree d admitting rational first integrals with fibers having geometric genus bounded by g.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":"1 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2016-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66815020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 13
Singularities of metrics on Hodge bundles and their topological invariants 霍奇束上度量的奇异性及其拓扑不变量
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2016-11-09 DOI: 10.14231/AG-2018-021
Dennis Eriksson, G. F. I. Montplet, Christophe Mourougane
{"title":"Singularities of metrics on Hodge bundles and their topological invariants","authors":"Dennis Eriksson, G. F. I. Montplet, Christophe Mourougane","doi":"10.14231/AG-2018-021","DOIUrl":"https://doi.org/10.14231/AG-2018-021","url":null,"abstract":"We consider degenerations of complex projective Calabi-Yau varieties and study the singularities of L2, Quillen and BCOV metrics on Hodge and determinant bundles. The dominant and subdominant terms in the expansions of the metrics close to non-smooth fibers are shown to be related to well-known topological invariants of singularities, such as limit Hodge structures, vanishing cycles and log-canonical thresholds. We also describe corresponding invariants for more general degenerating families in the case of the Quillen metric.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":"18 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2016-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66814559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
Strata of $k$-differentials k阶微分
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2016-10-28 DOI: 10.14231/AG-2019-011
Matt Bainbridge, Dawei Chen, Q. Gendron, S. Grushevsky, Martin Moeller
{"title":"Strata of $k$-differentials","authors":"Matt Bainbridge, Dawei Chen, Q. Gendron, S. Grushevsky, Martin Moeller","doi":"10.14231/AG-2019-011","DOIUrl":"https://doi.org/10.14231/AG-2019-011","url":null,"abstract":"A $k$-differential on a Riemann surface is a section of the $k$-th power of the canonical line bundle. Loci of $k$-differentials with prescribed number and multiplicities of zeros and poles form a natural stratification of the moduli space of $k$-differentials. In this paper we give a complete description for the compactification of the strata of $k$-differentials in terms of pointed stable $k$-differentials, for all $k$. The upshot is a global $k$-residue condition that can also be reformulated in terms of admissible covers of stable curves. Moreover, we study properties of $k$-differentials regarding their deformations, residues, and flat geometric structure.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":"1 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2016-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66814825","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 72
Satellites of spherical subgroups 球形亚群的卫星
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2016-10-24 DOI: 10.14231/ag-2020-004
V. Batyrev, Anne Moreau
{"title":"Satellites of spherical subgroups","authors":"V. Batyrev, Anne Moreau","doi":"10.14231/ag-2020-004","DOIUrl":"https://doi.org/10.14231/ag-2020-004","url":null,"abstract":"Let $G$ be a complex connected reductive algebraic group. Given a spherical subgroup $H subset G$ and a subset $I$ of the set of spherical roots of $G/H$, we define, up to conjugation, a spherical subgroup $H_I subset G$ of the same dimension of $H$, called a satellite. We investigate various interpretations of the satellites. We also show a close relation between the Poincare polynomials of the two spherical homogeneous spaces $G/H$ and $G/H_I$.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":"1 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2016-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66815929","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
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