{"id":"https://openalex.org/W7225320339","doi":"https://doi.org/10.48550/arxiv.2611.06862","title":"Heavy-Light Wall Crossings and Motivic Asymptotics of Moduli Spaces of Curves. Part I: Stabilization Graphs and Euler Characteristics","display_name":"Heavy-Light Wall Crossings and Motivic Asymptotics of Moduli Spaces of Curves. Part I: Stabilization Graphs and Euler Characteristics","publication_year":2026,"publication_date":"2026-11-04","ids":{"openalex":"https://openalex.org/W7225320339","doi":"https://doi.org/10.48550/arxiv.2611.06862"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2611.06862","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2611.06862","pdf_url":"https://arxiv.org/pdf/2611.06862","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2611.06862","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051138835","display_name":"Giordano Cotti","orcid":"https://orcid.org/0000-0002-9171-2569","observed_orcids":["https://orcid.org/0000-0002-9171-2569"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Cotti, Giordano","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5051138835"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9916999936103821,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9916999936103821,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.002300000051036477,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.00139999995008111,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/moduli-space-of-curves","display_name":"moduli space of curves","score":0.9470000267028809},{"id":"https://openalex.org/keywords/euler-characteristic","display_name":"Euler characteristic","score":0.8500000238418579},{"id":"https://openalex.org/keywords/wall-crossing","display_name":"wall-crossing","score":0.753000020980835},{"id":"https://openalex.org/keywords/deligne-mumford-compactification","display_name":"Deligne-Mumford compactification","score":0.9179999828338623},{"id":"https://openalex.org/keywords/graph-symmetry","display_name":"graph symmetry","score":0.6480000019073486},{"id":"https://openalex.org/keywords/asymptotic-expansion","display_name":"asymptotic expansion","score":0.5830000042915344},{"id":"https://openalex.org/keywords/genus-two","display_name":"genus two","score":0.6359999775886536},{"id":"https://openalex.org/keywords/genus-three","display_name":"genus three","score":0.8379999995231628}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7879999876022339},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.5741999745368958},{"id":"https://openalex.org/C73373263","wikidata":"https://www.wikidata.org/wiki/Q845677","display_name":"Moduli space","level":2,"score":0.5501999855041504},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.541100025177002},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.5144000053405762},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5016999840736389},{"id":"https://openalex.org/C196433757","wikidata":"https://www.wikidata.org/wiki/Q852973","display_name":"Euler characteristic","level":2,"score":0.48899999260902405},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.43380001187324524},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.41920000314712524},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.4185999929904938},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.415800005197525},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4124999940395355},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.31709998846054077},{"id":"https://openalex.org/C24209939","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic formula","level":2,"score":0.2994000017642975},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.2842000126838684},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.26930001378059387},{"id":"https://openalex.org/C134121241","wikidata":"https://www.wikidata.org/wiki/Q899301","display_name":"Yield (engineering)","level":2,"score":0.26100000739097595},{"id":"https://openalex.org/C2776299755","wikidata":"https://www.wikidata.org/wiki/Q432449","display_name":"Carry (investment)","level":2,"score":0.2554999887943268},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.25459998846054077},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2515999972820282},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.25110000371932983}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2611.06862","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2611.06862","pdf_url":"https://arxiv.org/pdf/2611.06862","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2611.06862","doi":"https://doi.org/10.48550/arxiv.2611.06862","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2611.06862","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2611.06862","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2611.06862","pdf_url":"https://arxiv.org/pdf/2611.06862","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7097834602","https://openalex.org/W2061456362","https://openalex.org/W4225597458","https://openalex.org/W2277967885","https://openalex.org/W7220962812","https://openalex.org/W4239480934","https://openalex.org/W2096008191","https://openalex.org/W7171701435","https://openalex.org/W4396814511","https://openalex.org/W2993670519"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,33,167,207],"develop":[4],"an":[5,119,123],"explicit":[6],"calculation":[7,36,67,114,126],"of":[8,13,84,96,143,163,186,204,222,231],"ordinary":[9,154,193,225],"topological":[10],"Euler":[11,155,226],"characteristics":[12,156],"the":[14,22,27,35,54,72,77,81,94,107,113,141,160,179,183,192,201,219],"coarse":[15],"moduli":[16],"spaces":[17,20],"underlying":[18],"Hassett":[19],"in":[21,68,76,115,118],"minimal":[23],"all-light":[24,152,223],"chamber":[25],"and":[26,44,62,89,99,131,190,213,236],"Deligne-Mumford":[28,78],"compactification.":[29],"For":[30,174],"genus":[31,69,116,177],"$g\\ge2$,":[32,178],"organize":[34],"through":[37],"a":[38,104,170,229],"decomposition":[39],"indexed":[40],"by":[41,159,169],"stabilization":[42],"graphs":[43,189],"their":[45,63,209],"decorations.":[46],"The":[47,66,149,197],"Burnside-Lefschetz":[48],"formula":[49],"allows":[50],"us":[51],"to":[52,147,153,224],"compute":[53],"resulting":[55],"contributions,":[56],"taking":[57],"into":[58],"account":[59],"graph":[60],"symmetries":[61],"fixed":[64,176],"loci.":[65],"two":[70],"illustrates":[71],"method":[73],"explicitly":[74],"and,":[75],"case,":[79],"recovers":[80],"generating":[82,210],"function":[83],"G.":[85,87,97],"Bini,":[86],"Gaiffi,":[88],"M.":[90],"Polito":[91],"(arXiv:math/9806048),":[92],"with":[93,122],"corrections":[95],"Bini":[98],"J.":[100],"Harer":[101],"(arXiv:math/0506083),":[102],"providing":[103],"check":[105],"on":[106,128],"construction.":[108],"We":[109,216],"also":[110,217],"carry":[111],"out":[112],"three":[117],"appendix.":[120],"Together":[121],"elementary":[124],"genus-one":[125],"based":[127],"collision":[129],"partitions":[130],"rational":[132,187],"necklaces,":[133],"these":[134,205],"formulas":[135],"yield":[136],"complete":[137],"asymptotic":[138,194,220],"expansions":[139],"as":[140],"number":[142],"labeled":[144],"markings":[145],"tends":[146],"infinity.":[148],"passage":[150],"from":[151],"is":[157],"governed":[158],"universal":[161],"change":[162],"variables":[164],"$\u03a6(z)=(2-z)e^z-2$,":[165],"which":[166],"derive":[168,208],"direct":[171],"wall-crossing":[172],"argument.":[173],"arbitrary":[175],"same":[180],"framework":[181],"identifies":[182],"leading":[184,198],"contribution":[185],"trivalent":[188],"gives":[191],"scale":[195],"$n!(e-2)^{-n}n^{(3g-5)/2}$.":[196],"constants":[199],"are":[200],"symmetry":[202],"weights":[203],"graphs;":[206],"function,":[211],"recurrence,":[212],"large-genus":[214],"behavior.":[215],"determine":[218],"ratio":[221],"characteristics,":[227],"answering":[228],"question":[230],"S.":[232,234],"Kannan,":[233],"Serpente,":[235],"C.":[237],"H.":[238],"Yun":[239],"(arXiv:2207.02800).":[240]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-11-06T00:00:00"}