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https://hdl.handle.net/10316/109860| Title: | On GIT quotients of Hilbert and Chow schemes of curves | Authors: | Bini, Gilberto Melo, Margarida Viviani, Filippo |
Keywords: | GIT; Hilbert scheme; Chow scheme; stable curves; pseudo-stable curves; compactified universal Jacobian | Issue Date: | 16-Sep-2011 | Publisher: | American Mathematical Society | Project: | The first named author has been partially supported by “FIRST” Universit`a di Milano and by MIUR PRIN 2010 - Variet`a algebriche: geometria, aritmetica e strutture di Hodge. The second named author was partially supported by CMUC and FCT (Portugal) through European program COMPETE/FEDER, by the FCT project Espa¸cos de Moduli em Geometria Alg´ebrica (PTDC/MAT/111332/2009), by the FCT project Geometria Alg´ebrica em Portugal (PTDC/MAT/099275/2008) and by the Funda¸c˜ao Calouste Gulbenkian program “Est´ımulo `a investiga ¸c˜ao 2010”. The third named author was partially supported by CMUC and FCT (Portugal) through European program COMPETE/FEDER and by the FCT project Espa¸cos de Moduli em Geometria Alg´ebrica (PTDC/MAT/111332/2009). | Serial title, monograph or event: | Electronic Research Announcements in Mathematical Sciences | Volume: | 19 | Issue: | 0 | Abstract: | The aim of this note is to announce some results on the GIT problem for the Hilbert and Chow scheme of curves of degree d and genus g in P^{d-g}, whose full details will appear in a subsequent paper. In particular, we extend the previous results of L. Caporaso up to d>4(2g-2) and we observe that this is sharp. In the range 2(2g-2)<d<7/2(2g-2), we get a complete new description of the GIT quotient. As a corollary, we get a new compactification of the universal Jacobian over the moduli space of pseudo-stable curves. | Description: | 8 pages, final version, to appear in Electron. Res. Announc. Math. Sci | URI: | http://hdl.handle.net/10316/109860 | ISSN: | 1935-9179 | DOI: | 10.3934/era.2012.19.33 | Rights: | openAccess |
| Appears in Collections: | FCTUC Matemática - Artigos em Revistas Internacionais |
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